A result on value distribution of L-functions

Li, Bao

doi:10.1090/S0002-9939-09-10222-8

A result on value distribution of L-functions
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by Bao Qin Li

Proc. Amer. Math. Soc. 138 (2010), 2071-2077

DOI: https://doi.org/10.1090/S0002-9939-09-10222-8

Published electronically: December 9, 2009

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Abstract:

We will establish a theorem on value distribution of L-functions in the Selberg class, which shows how an L-function and a meromorphic function are uniquely determined by their $c$-values and which, as a consequence, proves a result on the unicity of the Riemann zeta function.

References

Carlos A. Berenstein and Roger Gay, Complex variables, Graduate Texts in Mathematics, vol. 125, Springer-Verlag, New York, 1991. An introduction. MR 1107514, DOI 10.1007/978-1-4612-3024-3
E. Bombieri and A. Perelli, Distinct zeros of $L$-functions, Acta Arith. 83 (1998), no. 3, 271–281. MR 1611193, DOI 10.4064/aa-83-3-271-281
W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR 0164038
Liangwen Liao and Chung-Chun Yang, On some new properties of the gamma function and the Riemann zeta function, Math. Nachr. 257 (2003), 59–66. MR 1992811, DOI 10.1002/mana.200310078
Atle Selberg, Old and new conjectures and results about a class of Dirichlet series, Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989) Univ. Salerno, Salerno, 1992, pp. 367–385. MR 1220477
Jörn Steuding, Value-distribution of $L$-functions, Lecture Notes in Mathematics, vol. 1877, Springer, Berlin, 2007. MR 2330696