Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (4): 970-980.doi: 10.1007/s10473-020-0406-0

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UNIQUENESS THEOREMS OF L-FUNCTIONS IN THE EXTENDED SELBERG CLASS

Junfan CHEN1, Chunhui QIU2   

  1. 1. College of Mathematics and Informatics/Fujian Key Laboratory of Mathematical Analysis and Applications, Fujian Normal University, Fuzhou 350117, China;
    2. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2019-05-24 Revised:2019-07-31 Online:2020-08-25 Published:2020-08-21
  • Contact: Junfan CHEN E-mail:junfanchen@163.com
  • Supported by:
    The work was supported by the National Natural Science Foundation of China (11301076, 11571288 and 11971401), and the Natural Science Foundation of Fujian Province, China (2018J01658).

Abstract: We establish uniqueness theorems of L-functions in the extended Selberg class, which show how an L-function and a meromorphic function are uniquely determined by their shared values in two finite sets. This can be seen as a new solution of a problem proposed by Gross.

Key words: L-function, shared set, meromorphic function, uniqueness

CLC Number: 

  • 11M36
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