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A uniqueness theorem for functions in the extended Selberg class

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Abstract

We study the uniqueness of functions in the extended Selberg class. It was shown in Ki (Adv Math 231, 2484–2490, 2012) that if for a nonzero complex number \(c\) the inverse images \(L_1^{-1}(c)\) and \(L_2^{-1}(c)\) of two functions satisfying the same functional equation in the extended Selberg class are the same, then \(L_1(s)\) and \(L_2(s)\) are identical. Here we prove that this holds even without the assumption that they satisfy the same functional equation.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Rochester, Rochester, NY, 14627, USA

    Steven M. Gonek

  2. Department of Mathematics, Seoul National University, Seoul, Korea

    Jaeho Haan

  3. Department of Mathematics, Yonsei University, Seoul, 120-749, Korea

    Haseo Ki

  4. Korea Institute for Advanced Study, Seoul, Korea

    Haseo Ki

Authors
  1. Steven M. Gonek
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  2. Jaeho Haan
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  3. Haseo Ki
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Corresponding author

Correspondence to Haseo Ki.

Additional information

The third named author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and future Planning (2014R1A2A2A01002549).

Research of the first author was partially supported by NSF Grant DMS-1200582.

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Gonek, S.M., Haan, J. & Ki, H. A uniqueness theorem for functions in the extended Selberg class. Math. Z. 278, 995–1004 (2014). https://doi.org/10.1007/s00209-014-1343-1

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  • DOI: https://doi.org/10.1007/s00209-014-1343-1

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