Bulletin of the Korean Mathematical Society (대한수학회보)

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A CHARACTERIZATION OF L-FUNCTIONS IN THE EXTENDED SELBERG CLASS

  • Hu, Peichu (Department of Mathematics Shandong University) ;
  • Zhang, Pingyuan (Department of Mathematics Shandong University)
  • Received : 2015.10.14
  • Published : 2016.11.30
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Abstract

In this article, we establish a characterization of meromorphic functions and L-functions in the extended Selberg class, which shows that how they are uniquely determined by their c-values.

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References

  1. C. A. Berenstein and R. Gay, Complex variables, Spring, New York, 1991.
  2. E. Bombieri and A. Perelli, Distinct zeros of L-functions, Acta Arith. 83 (1998), no. 3, 271-281. https://doi.org/10.4064/aa-83-3-271-281
  3. W. K. Hayman, Meromorphic Functions, Oxford University Press, Oxford, 1964.
  4. J. Kaczorowski and A. Perelli, On the structure of the Selberg class. I. $0{\leq}d{\leq}1$, Acta Math. 182 (1999), no. 2, 207-241. https://doi.org/10.1007/BF02392574
  5. H. Ki and B. Q. Li, On uniqueness in the extended Selberg class of Dirichlet series, Proc. Amer. Math. Soc. 141 (2010), no. 12, 4169-4173. https://doi.org/10.1090/S0002-9939-2013-11749-1
  6. B. Q. Li, A result on value distribution of L-functions, Proc. Amer. Math. Soc. 138 (2010), no. 6, 2071-2077. https://doi.org/10.1090/S0002-9939-09-10222-8
  7. B. Q. Li, A uniqueness theorem for Dirichlet series satisfying a Riemann type functional equation, Adv. Math. 226 (2011), no. 5, 4198-4211. https://doi.org/10.1016/j.aim.2010.12.001
  8. X. M. Li and H. X. Yi, Results on value distribution of L-functions, Math. Nachr. 286 (2013), no. 13, 1326-1336. https://doi.org/10.1002/mana.201200196
  9. A. Selberg, Old and new conjectures and results about a class of Dirichlet series, in: Proceedings of the Amalfi Conference on Analytic Number Theory (Maiori, 1989), 367-385, Univ. Salerno, Salerno, 1992.
  10. J. Steuding, Value-distribution of L-functions, Spinger, Berlin, 2007.
  11. A. D. Wu and P. C. Hu, Uniqueness theorems for Dirichlet series, Bull. Aus. Math. Soc. 91 (2015), 389-399. https://doi.org/10.1017/S0004972714001166
  12. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, London, 2003.
  13. P. C. Hu and B. Q. Li, A simple proof and strengthening of a uniqueness theorem for L-functions, Canad. Math. Bull. 59 (2016), no. 1, 119-122. https://doi.org/10.4153/CMB-2015-045-1