In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we...In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.展开更多
Based on general relativity, J. R. Oppenheimer proved that massive celestial bodies may collapse into singular black holes with infinite densities. By analyzing the original paper of Oppenheimer, this paper reveals th...Based on general relativity, J. R. Oppenheimer proved that massive celestial bodies may collapse into singular black holes with infinite densities. By analyzing the original paper of Oppenheimer, this paper reveals that the calculations had a series and serious of mistakes. The basic problem is that the calculation supposes that the density of celestial body does not change with space-time coordinates. The density is firstly assumed invariable with space coordinates and then it is assumed invariable with time. But at last, the conclusion that the density of a celestial body becomes infinity is deduced. The premise contradicts with conclusion. In fact, there is no restriction on the initial density and radius for celestial body in the calculation. According to the calculation results of Oppenheimer, a cloud of thin gas may also collapse into singular black hole under the action of gravity. The calculations neglect great rotating speeds of massive and high density celestial bodies which would make them falling apart rather than collapsing into singularities. Because we do not know the function relations that material densities depend on space-time coordinates in advance, there exists the rationality problem of procedure using the Einstein’s equation of gravity field to calculate material collapse. Besides these physical problems, the calculation of Oppenheimer also has some obvious mistakes in mathematics. Another improved method to calculate massive celestial body’s collapse also has similar problems. The results are also unreliable. The conclusion of this paper is that up to now general relativity actually has not proved that massive celestial bodies may collapse into singularity black holes.展开更多
It is proved strictly based on general relativity that two important factors are neglected in LIGO experiments by using Michelson interferometers so that fatal mistakes were caused. One is that the gravitational wave ...It is proved strictly based on general relativity that two important factors are neglected in LIGO experiments by using Michelson interferometers so that fatal mistakes were caused. One is that the gravitational wave changes the wavelength of light. Another is that light’s speed is not a constant when gravitational waves exist. According to general relativity, gravitational wave affects spatial distance, so it also affects the wavelength of light synchronously. By considering this fact, the phase differences of lasers were invariable when gravitational waves passed through Michelson interferometers. In addition, when gravitational waves exist, the spatial part of metric changes but the time part of metric is unchanged. In this way, light’s speed is not a constant. When the calculation method of time difference is used in LIGO experiments, the phase shift of interference fringes is still zero. So the design principle of LIGO experiment is wrong. It was impossible for LIGO to detect gravitational wave by using Michelson interferometers. Because light’s speed is not a constant, the signals of LIGO experiments become mismatching. It means that these signals are noises actually, caused by occasional reasons, no gravitational waves are detected really. In fact, in the history of physics, Michelson and Morley tried to find the absolute motion of the earth by using Michelson interferometers but failed at last. The basic principle of LIGO experiment is the same as that of Michelson-Morley experiment in which the phases of lights were invariable. Only zero result can be obtained, so LIGO experiments are destined failed to find gravitational waves.展开更多
By transforming the geodesic equation of the Schwarzschild solution of the Einstein’s equation of gravity field to flat space-time for description, the revised Newtonian formula of gravity is obtained. The formula ca...By transforming the geodesic equation of the Schwarzschild solution of the Einstein’s equation of gravity field to flat space-time for description, the revised Newtonian formula of gravity is obtained. The formula can also describe the motion of object with mass in gravity field such as the perihelion precession of the Mercury. The space-time singularity in the Einstein’s theory of gravity becomes the original point r = 0 in the Newtonian formula of gravity. The singularity problem of gravity in curved space-time is eliminated thoroughly. When the formula is used to describe the expansive universe, the revised Friedmann equation of cosmology is obtained. Based on it, the high red-shift of Ia supernova can be explained well. We do not need the hypotheses of the universe accelerating expansion and dark energy again. It is also unnecessary for us to assume that non-baryon dark material is 5 - 6 times more than normal baryon material in the universe if they really exist. The problem of the universal age can also be solved well. The theory of gravity returns to the traditional form of dynamic description and becomes normal one. The revised equation can be taken as the foundation of more rational cosmology.展开更多
There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photo...There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photon. The third is the Doppler’s effect which is related to velocity. The basic formula used to calculate the relation of red shift and distance of Ia supernova in cosmology is which is related to the scalar factor of the R-W metric. It is completely different from the Doppler formula of red shift which is related to velocity factor . This kind of inconsistency is not allowed in physics. Because of , when became larger and larger with time increase, z became smaller and smaller, means that space expansion leads to red shift becoming smaller. At present time, we have and , means that there is no red shift for the light emitted from distance celestial bodies at present. The results obviously violate the Hubble law! It is proved strictly in mathematics that the formula is untenable unless constant and . The further study reveals that the essential reason of the mistake is that the R-W metric violates the principle of light’s speed invariable. The time delay caused by relativity velocity between light’s source and observer is neglected. Besides, there exists the problem of time misalignment between theoretical calculation and practical observations in the original documents of Ia supernova projects. So the formula used to calculate the relation between red shift and distance of Ia supernova is wrong and the deduced conclusion about dark energy and the accelerating expansion of the universe are incredible. It is proved in this paper that based on the Doppler’s formula and the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating expansion of the universe are completely unnecessary in cosmology.展开更多
The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to ca...The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes.展开更多
It is proved in this paper that Abel’s and Galois’s proofs that the quintic equations have no radical solutions are invalid. Due to Abel’s and Galois’s work about two hundred years ago, it was generally accepted t...It is proved in this paper that Abel’s and Galois’s proofs that the quintic equations have no radical solutions are invalid. Due to Abel’s and Galois’s work about two hundred years ago, it was generally accepted that general quintic equations had no radical solutions. However, Tang Jianer <i><span style="font-family:Verdana;font-size:12px;">et</span></i><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> recently prove that there are radical solutions for some quintic equations with special forms. The theories of Abel and Galois cannot explain these results. On the other hand, Gauss </span><i><span style="font-family:Verdana;font-size:12px;">et</span></i></span><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> proved the fundamental theorem of algebra. The theorem declared that there were </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> solutions for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> degree equations, including the radical and non-radical solutions. The theories of Abel and Galois contradicted with the fundamental theorem of algebra. Due to the reasons above, the proofs of Abel and Galois should be re-examined and re-evaluated. The author carefully analyzed the Abel’s original paper and found some serious mistakes. In order to prove that the general solution of algebraic equation</span></span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">he proposed was effective for the cubic equation, Abel took the known solutions of cubic equation as a premise to calculate the parameters of his equation. Therefore, Abel’s proof is a logical circular argument and invalid. Besides, Abel confused the variables with the coefficients (constants) of algebraic equations. An expansion with 14 terms was written as 7 terms, 7 terms were missing.</span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">We prefer to consider Galois’s theory as a hypothesis rather than a proof. Based on that permutation group </span><i><span style="font-size:12px;font-family:Verdana;">S</span></i><sub><span style="font-size:12px;font-family:Verdana;">5</span></sub><span style="font-size:12px;font-family:Verdana;"> had no true normal subgroup, Galois concluded that the quintic equations had no radical solutions, but these two problems had no inevitable logic connection actually. In order to prove the effectiveness of radical extension group of automorphism mapping for the cubic and quartic equations, in the Galois’s theory, some algebraic relations among the roots of equations were used to replace the root itself. This violated the original definition of automorphism mapping group, led to the confusion of concepts and arbitrariness. For the general cubic and quartic algebraic equations, the actual solving processes do not satisfy the tower structure of Galois’s solvable group. The resolvents of cubic and quartic equations are proved to have no symmetries of Galois’s soluble group actually. It is invalid to use the solvable group theory to judge whether the high degree equation has a radical solution. The conclusion of this paper is that there is only the </span><i><span style="font-size:10.0pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;">S</span><sub><span style="font-family:Verdana;font-size:12px;">n</span></sub></span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> symmetry for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> degree algebraic equations. The symmetry of Galois’s solvable group does not exist. Mathematicians should get rid of the constraints of Abel and Galois’s theories, keep looking for the radical solutions of high degree equations.</span></span>展开更多
A standard method is proposed to prove strictly that the Riemann Zeta function equation has no non-trivial zeros. The real part and imaginary part of the Riemann Zeta function equation are separated completely. Suppo...A standard method is proposed to prove strictly that the Riemann Zeta function equation has no non-trivial zeros. The real part and imaginary part of the Riemann Zeta function equation are separated completely. Suppose ξ(s) = ξ1(a,b) + iξ2(a,b) = 0 but ζ(s) = ζ1(a,b) + iζ2(a,b) ≠ 0 with s = a + ib at first. By comparing the real part and the imaginary part of Zeta function equation individually, a set of equation about a and b is obtained. It is proved that this equation set only has the solutions of trivial zeros. In order to obtain possible non-trivial zeros, the only way is to suppose that ζ1(a,b) = 0 and ζ2(a,b) = 0. However, by using the compassion method of infinite series, it is proved that ζ1(a,b) ≠ 0 and ζ2(a,b) ≠ 0. So the Riemann Zeta function equation has no non-trivial zeros. The Riemann hypothesis does not hold.展开更多
文摘In the classical Newtonian mechanics, the gravity fields of static thin loop and double spheres are two simple but foundational problems. However, in the Einstein’s theory of gravity, they are not simple. In fact, we do not know their solutions up to now. Based on the coordinate transformations of the Kerr and the Kerr-Newman solutions of the Einstein’s equation of gravity field with axial symmetry, the gravity fields of static thin loop and double spheres are obtained. The results indicate that, no matter how much the mass and density are, there are singularities at the central point of thin loop and the contact point of double spheres. What is more, the singularities are completely exposed in vacuum. Space near the surfaces of thin loop and spheres are highly curved, although the gravity fields are very weak. These results are inconsistent with practical experience and completely impossible. By reasonable analogy, black holes with singularity in cosmology and astrophysics are something illusive. Caused by the mathematical description of curved space-time, they do not exist in real world actually. If there are black holes in the universe, they can only be the types of the Newtonian black holes without singularities, rather than the Einstein’s singularity black holes. In order to escape the puzzle of singularity thoroughly, the description of gravity should return to the traditional form of dynamics in flat space. The renormalization of gravity and the unified description of four basic interactions may be possible only based on the frame of flat space-time. Otherwise, theses problems can not be solved forever. Physicists should have a clear understanding about this problem.
文摘Based on general relativity, J. R. Oppenheimer proved that massive celestial bodies may collapse into singular black holes with infinite densities. By analyzing the original paper of Oppenheimer, this paper reveals that the calculations had a series and serious of mistakes. The basic problem is that the calculation supposes that the density of celestial body does not change with space-time coordinates. The density is firstly assumed invariable with space coordinates and then it is assumed invariable with time. But at last, the conclusion that the density of a celestial body becomes infinity is deduced. The premise contradicts with conclusion. In fact, there is no restriction on the initial density and radius for celestial body in the calculation. According to the calculation results of Oppenheimer, a cloud of thin gas may also collapse into singular black hole under the action of gravity. The calculations neglect great rotating speeds of massive and high density celestial bodies which would make them falling apart rather than collapsing into singularities. Because we do not know the function relations that material densities depend on space-time coordinates in advance, there exists the rationality problem of procedure using the Einstein’s equation of gravity field to calculate material collapse. Besides these physical problems, the calculation of Oppenheimer also has some obvious mistakes in mathematics. Another improved method to calculate massive celestial body’s collapse also has similar problems. The results are also unreliable. The conclusion of this paper is that up to now general relativity actually has not proved that massive celestial bodies may collapse into singularity black holes.
文摘It is proved strictly based on general relativity that two important factors are neglected in LIGO experiments by using Michelson interferometers so that fatal mistakes were caused. One is that the gravitational wave changes the wavelength of light. Another is that light’s speed is not a constant when gravitational waves exist. According to general relativity, gravitational wave affects spatial distance, so it also affects the wavelength of light synchronously. By considering this fact, the phase differences of lasers were invariable when gravitational waves passed through Michelson interferometers. In addition, when gravitational waves exist, the spatial part of metric changes but the time part of metric is unchanged. In this way, light’s speed is not a constant. When the calculation method of time difference is used in LIGO experiments, the phase shift of interference fringes is still zero. So the design principle of LIGO experiment is wrong. It was impossible for LIGO to detect gravitational wave by using Michelson interferometers. Because light’s speed is not a constant, the signals of LIGO experiments become mismatching. It means that these signals are noises actually, caused by occasional reasons, no gravitational waves are detected really. In fact, in the history of physics, Michelson and Morley tried to find the absolute motion of the earth by using Michelson interferometers but failed at last. The basic principle of LIGO experiment is the same as that of Michelson-Morley experiment in which the phases of lights were invariable. Only zero result can be obtained, so LIGO experiments are destined failed to find gravitational waves.
文摘By transforming the geodesic equation of the Schwarzschild solution of the Einstein’s equation of gravity field to flat space-time for description, the revised Newtonian formula of gravity is obtained. The formula can also describe the motion of object with mass in gravity field such as the perihelion precession of the Mercury. The space-time singularity in the Einstein’s theory of gravity becomes the original point r = 0 in the Newtonian formula of gravity. The singularity problem of gravity in curved space-time is eliminated thoroughly. When the formula is used to describe the expansive universe, the revised Friedmann equation of cosmology is obtained. Based on it, the high red-shift of Ia supernova can be explained well. We do not need the hypotheses of the universe accelerating expansion and dark energy again. It is also unnecessary for us to assume that non-baryon dark material is 5 - 6 times more than normal baryon material in the universe if they really exist. The problem of the universal age can also be solved well. The theory of gravity returns to the traditional form of dynamic description and becomes normal one. The revised equation can be taken as the foundation of more rational cosmology.
文摘There are three main mechanisms to cause the red shift of spectrum in physics. The first is gravity which is related to mass. The second is the Compton scattering which is related to the energy transformation of photon. The third is the Doppler’s effect which is related to velocity. The basic formula used to calculate the relation of red shift and distance of Ia supernova in cosmology is which is related to the scalar factor of the R-W metric. It is completely different from the Doppler formula of red shift which is related to velocity factor . This kind of inconsistency is not allowed in physics. Because of , when became larger and larger with time increase, z became smaller and smaller, means that space expansion leads to red shift becoming smaller. At present time, we have and , means that there is no red shift for the light emitted from distance celestial bodies at present. The results obviously violate the Hubble law! It is proved strictly in mathematics that the formula is untenable unless constant and . The further study reveals that the essential reason of the mistake is that the R-W metric violates the principle of light’s speed invariable. The time delay caused by relativity velocity between light’s source and observer is neglected. Besides, there exists the problem of time misalignment between theoretical calculation and practical observations in the original documents of Ia supernova projects. So the formula used to calculate the relation between red shift and distance of Ia supernova is wrong and the deduced conclusion about dark energy and the accelerating expansion of the universe are incredible. It is proved in this paper that based on the Doppler’s formula and the method of numerical calculation, the relation of red shift and distance of Ia supernova can be explained well. The hypotheses of dark energy and the accelerating expansion of the universe are completely unnecessary in cosmology.
文摘The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes.
文摘It is proved in this paper that Abel’s and Galois’s proofs that the quintic equations have no radical solutions are invalid. Due to Abel’s and Galois’s work about two hundred years ago, it was generally accepted that general quintic equations had no radical solutions. However, Tang Jianer <i><span style="font-family:Verdana;font-size:12px;">et</span></i><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> recently prove that there are radical solutions for some quintic equations with special forms. The theories of Abel and Galois cannot explain these results. On the other hand, Gauss </span><i><span style="font-family:Verdana;font-size:12px;">et</span></i></span><i><span style="font-size:12px;font-family:Verdana;"> al</span><span style="font-size:12px;font-family:Verdana;">.</span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> proved the fundamental theorem of algebra. The theorem declared that there were </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> solutions for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> degree equations, including the radical and non-radical solutions. The theories of Abel and Galois contradicted with the fundamental theorem of algebra. Due to the reasons above, the proofs of Abel and Galois should be re-examined and re-evaluated. The author carefully analyzed the Abel’s original paper and found some serious mistakes. In order to prove that the general solution of algebraic equation</span></span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">he proposed was effective for the cubic equation, Abel took the known solutions of cubic equation as a premise to calculate the parameters of his equation. Therefore, Abel’s proof is a logical circular argument and invalid. Besides, Abel confused the variables with the coefficients (constants) of algebraic equations. An expansion with 14 terms was written as 7 terms, 7 terms were missing.</span><span style="font-size:10pt;font-family:;" "=""> </span><span style="font-size:12px;font-family:Verdana;">We prefer to consider Galois’s theory as a hypothesis rather than a proof. Based on that permutation group </span><i><span style="font-size:12px;font-family:Verdana;">S</span></i><sub><span style="font-size:12px;font-family:Verdana;">5</span></sub><span style="font-size:12px;font-family:Verdana;"> had no true normal subgroup, Galois concluded that the quintic equations had no radical solutions, but these two problems had no inevitable logic connection actually. In order to prove the effectiveness of radical extension group of automorphism mapping for the cubic and quartic equations, in the Galois’s theory, some algebraic relations among the roots of equations were used to replace the root itself. This violated the original definition of automorphism mapping group, led to the confusion of concepts and arbitrariness. For the general cubic and quartic algebraic equations, the actual solving processes do not satisfy the tower structure of Galois’s solvable group. The resolvents of cubic and quartic equations are proved to have no symmetries of Galois’s soluble group actually. It is invalid to use the solvable group theory to judge whether the high degree equation has a radical solution. The conclusion of this paper is that there is only the </span><i><span style="font-size:10.0pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;">S</span><sub><span style="font-family:Verdana;font-size:12px;">n</span></sub></span></i><span style="font-size:10pt;font-family:;" "=""><span style="font-family:Verdana;font-size:12px;"> symmetry for the </span><i><span style="font-family:Verdana;font-size:12px;">n</span></i><span style="font-family:Verdana;font-size:12px;"> degree algebraic equations. The symmetry of Galois’s solvable group does not exist. Mathematicians should get rid of the constraints of Abel and Galois’s theories, keep looking for the radical solutions of high degree equations.</span></span>
文摘A standard method is proposed to prove strictly that the Riemann Zeta function equation has no non-trivial zeros. The real part and imaginary part of the Riemann Zeta function equation are separated completely. Suppose ξ(s) = ξ1(a,b) + iξ2(a,b) = 0 but ζ(s) = ζ1(a,b) + iζ2(a,b) ≠ 0 with s = a + ib at first. By comparing the real part and the imaginary part of Zeta function equation individually, a set of equation about a and b is obtained. It is proved that this equation set only has the solutions of trivial zeros. In order to obtain possible non-trivial zeros, the only way is to suppose that ζ1(a,b) = 0 and ζ2(a,b) = 0. However, by using the compassion method of infinite series, it is proved that ζ1(a,b) ≠ 0 and ζ2(a,b) ≠ 0. So the Riemann Zeta function equation has no non-trivial zeros. The Riemann hypothesis does not hold.
