In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which includ...In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.展开更多
In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-...In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.展开更多
In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theor...In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.展开更多
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu...In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.展开更多
Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（...Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（z）） = E（aj,M（z）） （j = 1,..., 2v ＋ 2k ＋ 1） holds in the angular domain Ω（θ-δ,θ-δ）, where b, aj （j = 1,..., 2v -b 2k -k 1） are complex constants. The same results axe obtained for the case that△（θ） is a Borel direction of order ∞ （or ρ（τ）） of W（z） （or M（z））.展开更多
We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ countin...We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of Jank-Mues-Volkmann.Our method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding vectors.This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the functions.Furthermore,the idea in this paper can also be applied to the case for several variables.展开更多
In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some exam...In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.展开更多
Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.
In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and ...In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.展开更多
基金supported by the Natural Science Foundation of China(11871108)Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhai+2 种基金Guangdong Natural Science Foundation(2018A030313954)Guangdong Universities(Basic Research and Applied Research)Major Project(2017KZDXM038)Guangdong Provincical Anti-monopoly Law Enforcement and Big Data Analysis Research Center Project(2019D04)。
文摘In this article,we discuss,by Nevanlinna theory,the influence of multiple values and deficiencies on the uniqueness problem of algebroid functions.We get several uniqueness theorems of algebroid functions which include an at most 3v-valued theorem.These results extend the existing achievements of some scholars.
基金The NSF (10471048) of Chinathe Research Fund (20050574002) for the DoctoralProgram of Higher Education
文摘In this paper, the uniqueness of algebroidal functions in the unit disc is investigated. Suppose that W（z） and M（z） are v-valued and k-valued algebroidal functions in the unit disc, respectively. Let e^iθ be a b-cluster point of order co or order ρ（x） of the algebroidal function W（z） or M（z）. It is shown that if -↑E（aj, W（z）） = -↑E（aj,M（z）） holds in the domain {｜z｜ 〈 1}∩Ω（θ-δ,θ＋δ）, where b, aj （j = 1,…, 2v ＋ 2k ＋ 1） are complex constants, then W（z） = M（z）. The same results are obtained for the case that e^iθ is a Borel point of order co or order ρ（x） of the algebroidal function W（z） or M（z）.
基金Supported by the NNSF of China(10471048)Supported by the Doctoral Foundation of the Education Committee of China(20050574002)
文摘In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.
基金Supported by the NNSFC (10671109)the NSFFC(2008J0190)+1 种基金the Research Fund for Talent Introduction of Ningde Teachers College (2009Y019)the Scitific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.
基金Supported by the National Natural Science Foundation of China (Grant No. 10471048)the Research Fund of the Doctoral Program of Higher Education (Grant No. 20050574002)
文摘Let W（z） and M（z） be v-valued and k-valued algebroidal functions respectively △（θ） be a b-cluster line of order ∞ （or ρ（r）） of W（z） （or M（z））. It is shown that W（z） ≡ M（z） provided E（aj, W（z）） = E（aj,M（z）） （j = 1,..., 2v ＋ 2k ＋ 1） holds in the angular domain Ω（θ-δ,θ-δ）, where b, aj （j = 1,..., 2v -b 2k -k 1） are complex constants. The same results axe obtained for the case that△（θ） is a Borel direction of order ∞ （or ρ（τ）） of W（z） （or M（z））.
基金Supported by National Natural Science Foundation of China(Grant Nos.12071047,12171127,11901311)National Key Technologies R&D Program of China(Grant No.2020YFA0713300)。
文摘We investigate the uniqueness problems of meromorphic functions and their difference operators by using a new method.It is proved that if a non-constant meromorphic function f shares a non-zero constant and ∞ counting multiplicities with its difference operators Δcf(z) and Δ_(c)^(2)f(z), thenΔcf(z)≡Δ_(c)^(2)f(z).In particular,we give a difference analogue of a result of Jank-Mues-Volkmann.Our method has two distinct features:(ⅰ) It converts the relations between functions into the corresponding vectors.This makes it possible to deal with the uniqueness problem by linear algebra and combinatorics.(ⅱ) It circumvents the obstacle of the difference logarithmic derivative lemma for meromorphic functions of infinite order,since this method does not depend on the growth of the functions.Furthermore,the idea in this paper can also be applied to the case for several variables.
基金supported by the National Natural Science Foundation of China(10771121,11301220,11371225)the Tianyuan Fund for Mathematics(11226094)+2 种基金the NSF of Shandong Province,China(ZR2012AQ020,ZR2010AM030)the Fund of Doctoral Program Research of Shaoxing College of Art and Science(20135018)the Fund of Doctoral Program Researchof University of Jinan(XBS1211)
文摘In this article, we investigate the uniqueness problems of difference polynomials of meromorphic functions and obtain some results which can be viewed as discrete analogues of the results given by Shibazaki. Some examples are given to show the results in this article are best possible.
文摘Using the Nevanlinna theory of the value distribution of meromorphic functions, we investigate the existence problem of admissible algebroid solutions of generalized higher order algebraic differential equations.
基金supported by NSFC (10871076,10771011)SRFDP (20050574002)NKBRP (2005CB321902)
文摘In this article, we first investigate the operational properties of algebroid functions. Then we prove two uniqueness theorems for algebroid functions.
基金supported by NSF of China (11209119511171119+1 种基金11101096)the STP of Education Department of Jiangxi Province,China (GJJ12179)
文摘In this paper, we define the shared value of an algebroid function and its derivative on its Riemann surface. By considering the relationship between the shared values and the branch points of algebroid functions and their derivatives, we obtain some uniqueness theorems of algebroid functions sharing values with their derivatives, which extend 3 IM shared values theorem of nonconstant meromorphic functions and their derivatives obtained by Mues-Steinmetz and Gundersen.
