In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditio...In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.展开更多
Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equatio...Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.展开更多
An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolu...An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.展开更多
This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specific...This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.展开更多
In this paper,we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture.We prove,for some special connected fractal domains,the sharp estimate for second term of counting function asymp...In this paper,we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture.We prove,for some special connected fractal domains,the sharp estimate for second term of counting function asymptotics,which implies that the weak form of the Weyl- Berry conjecture holds for the case.Finally,we also study a naturally connected fractal domain,and we prove,in this case,the weak Weyl-Berry conjecture holds as well.展开更多
For a cubic algebraic extension K of Q, the behavior of the ideal counting function is considered in this paper. More precisely, let aK（n） be the number of integral ideals of the field K with norm n, we prove an asy...For a cubic algebraic extension K of Q, the behavior of the ideal counting function is considered in this paper. More precisely, let aK（n） be the number of integral ideals of the field K with norm n, we prove an asymptotic formula for the sum.展开更多
We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex dif...We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.展开更多
We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IR<sup>n</sup>（n≥2） with non-smoot...In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IR<sup>n</sup>（n≥2） with non-smooth boundaryΩ and connected complement Ω<sub>e</sub>=IR<sup>n</sup>\.We can prove that if Ω satisfies a certain geometrical condition,then where φ（λ）=[（4π）<sup>n/2</sup>Γ(1+（n/2）]<sup>-1</sup>|Ω|<sub>n</sub>λ<sup>n/2</sup>,d<sub>n</sub>】0 depending only on n,and |·|<sub>j</sub>（j=n-1,n）is a j-dimensional Lebesgue measure.展开更多
Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T（x） be the numb...Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T（x） be the number of terms of T not exceeding x. In 1994, Sarkozy and Szemer′edi confirmed a conjecture of Danzer by proving that, for infinite additive complements A and B, if lim sup A（x）B（x）/x 1, then A（x）B（x）-x → ＋∞ as x → ＋∞. In this paper, it is proved that, if A and B are infinite additive complements with lim sup A（x）B（x）/x〈（√4 ＋ 2）/7 = 1.093 …, then（A（x）B（x）-x）/min{A（x）, B（x）} → ＋∞ as x → ＋∞.展开更多
基金supported by the National Natural Science Foundation of China(12171373)Chen's work also supported by the Fundamental Research Funds for the Central Universities of China(GK202207018).
文摘In this paper,we study composition operators on weighted Bergman spaces of Dirichlet series.We first establish some Littlewood-type inequalities for generalized mean counting functions.Then we give sufficient conditions for a composition operator with zero characteristic to be bounded or compact on weighted Bergman spaces of Dirichlet series.The corresponding sufficient condition for compactness in the case of positive characteristics is also obtained.
基金Supported by the National Natural Science Foundation of China（10471065） Supported by the Natural Science Foundation of Guangdong Province（04010474）
文摘Using Nevanlinna theory and value distribution of meromorphic functions and the other techniques,we investigate the counting functions of meromorphic solutions of systems of higher-order algebraic differential equations and obtain some results.
文摘An independent method for paper [10] is presented. Weighted lattice paths are enumerated by counting function which is a natural extension of Gaussian multinomial coefficient in the case of unrestricted paths. Convolutions for path counts are investigated, which yields some Vandcrmondc-type identities for multinomial and q-multinomial coefficients.
文摘This paper attempts to form a bridge between a sum of the divisors function and the gamma function, proposing a novel approach that could have significant implications for classical problems in number theory, specifically the Robin inequality and the Riemann hypothesis. The exploration of using invariant properties of these functions to derive insights into twin primes and sequential primes is a potentially innovative concept that deserves careful consideration by the mathematical community.
基金Research partially supported by the Natural Science Foundation of China and the Royal Society of London
文摘In this paper,we study the spectral asymptotics for connected fractal domains and Weyl-Berry conjecture.We prove,for some special connected fractal domains,the sharp estimate for second term of counting function asymptotics,which implies that the weak form of the Weyl- Berry conjecture holds for the case.Finally,we also study a naturally connected fractal domain,and we prove,in this case,the weak Weyl-Berry conjecture holds as well.
文摘For a cubic algebraic extension K of Q, the behavior of the ideal counting function is considered in this paper. More precisely, let aK（n） be the number of integral ideals of the field K with norm n, we prove an asymptotic formula for the sum.
基金Project Supported by the Natural Science Foundation of China (10471065)the Natural Science Foundation of Guangdong Province (04010474)
文摘We apply Nevanlinna theory of the value distribution of meromorphic functions to study the properties of Nevanlinna counting function and proximity function of meromorphic solutions of a type of systems of complex difference equations. Our results can give estimates on the proximity function and the counting function of solutions of systems of difference equations. This implies that solutions have a relatively large number of poles. It extend some result concerning difference equations to the systems of difference equations.
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
基金Research partially supported by the Natural Science Foundation of Chinathe Grant of Chinese State Education Committee
文摘In this paper,we study the asymptotic behaviour of the scattering phase s（λ）of the Dirichlet Laplacian associated with obstacle,where Ω is a bounded open subset of IR<sup>n</sup>（n≥2） with non-smooth boundaryΩ and connected complement Ω<sub>e</sub>=IR<sup>n</sup>\.We can prove that if Ω satisfies a certain geometrical condition,then where φ（λ）=[（4π）<sup>n/2</sup>Γ(1+（n/2）]<sup>-1</sup>|Ω|<sub>n</sub>λ<sup>n/2</sup>,d<sub>n</sub>】0 depending only on n,and |·|<sub>j</sub>（j=n-1,n）is a j-dimensional Lebesgue measure.
基金supported by National Natural Science Foundation of China (Grant Nos. 11671211 and 11371195)the China Scholarship Council (Grant No. 201608320048)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘Two infinite sequences A and B of non-negative integers are called infinite additive complements if their sum contains all sufficiently large integers. For a sequence T of non-negative integers, let T（x） be the number of terms of T not exceeding x. In 1994, Sarkozy and Szemer′edi confirmed a conjecture of Danzer by proving that, for infinite additive complements A and B, if lim sup A（x）B（x）/x 1, then A（x）B（x）-x → ＋∞ as x → ＋∞. In this paper, it is proved that, if A and B are infinite additive complements with lim sup A（x）B（x）/x〈（√4 ＋ 2）/7 = 1.093 …, then（A（x）B（x）-x）/min{A（x）, B（x）} → ＋∞ as x → ＋∞.
