李效敏,杜现瑞

• 1:中国海洋大学数学科学学院

摘要(Abstract)：

本文研究了满足公理(i)～(iii)的L-函数与其移动算子CM分担一个非零有限值的唯一性问题。本文所得结果推广和改进了J. Steuding(2007年)和李宝勤(2011年)的有关结果，并举例说明本文得到的主要定理的有关条件是最佳的。

关键词(KeyWords)： 差分Nevanlinna理论;亚纯函数;L-函数;唯一性定理

Abstract:

Keywords:

基金项目(Foundation): 中央高校基本科研业务费专项(3016000841964007);; 山东省自然科学基金项目(ZR2019MA029)资助~~

作者(Author): 李效敏,杜现瑞

DOI: 10.16441/j.cnki.hdxb.20210287

参考文献(References)：

• [1] Hayman W K.Meromorphic Functions[M].Oxford:Clarendon Press,1964.
• [2] 仪洪勋，杨重骏.亚纯函数的唯一性理论[M].北京：科学出版社，1995.Yi H X,Yang C C.Uniqueness Theory of Meromorphic Functions[M].Beijing:Science Press,1995.
• [3] Steuding J.Value Distribution of L-Functions[M].Berlin:Springer-Verlag,2007.
• [4] Selberg A.Old and New Conjectures and Results about a Class of Dirichlet Series[C].Berlin:Springer-Verlag,1991:47-63.
• [5] Kaczorowski J,Perelli A.On the structure of the Selberg class 0≤d ≤1[J].Acta Mathematica,1999,182(2):207-241.
• [6] Hu P C,Li B Q.A simple proof and strengthening of a uniqueness theorem for L-functions[J].Canadian Mathematical Bulletin,2016,59(1):119-122.
• [7] Li B Q.A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation[J].Advances in Mathematics,2011,226(5):4198-4211.
• [8] Halburd R G,Korhonen R J.Nevanlinna theory for the difference operator[J].Annales- Academiae Scientiarum Fennicae Mathematica,2005,31(2):463-478.
• [9] Halburd R G,Korhonen R J.Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].Journal of Mathematical Analysis and Applications,2006,314(2):477-487.
• [10] Chiang Y M,Feng S J.On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane[J].Ramanujan Journal,2008,16(1):105-129.
• [11] Laine I,Yang C C.Clunie theorems for difference and q-difference polynomials[J].Journal of the London Mathematical Society,2007,76(3):556-566.
• [12] Heittokangas J,Korhonen R,Laine I,et al.Value sharing results for shifts of meromorphic functions and sufficient conditions for periodicity[J].Journal of Mathematical Analysis and Applications,2009,355(1):352-363.
• [13] Heittokangas J,Korhonen R,Laine I,et al.Uniqueness of meromorphic functions sharing values with their shifts[J].Complex Variables & Elliptic Equations An International Journal,2011,56(1-4):81-92.
• [14] Lü F,Lü W R.On the uniqueness of entire functions having Dirichlet series representations[J].Mathematische Nachrichten,2021,294(9):1773-1782.
• [15] Markushevich A I.Theory of Functions of a Complex Variable Vol Ⅱ[M].Silverman A translated.English Revised Edition.Englewood Cliffs:Prentice Hall,1965.

文章评论(Comment)：