A uniqueness theorem for functions in the extended Selberg class

Steven M Gonek,Haseo Ki,Jaeho Haan

doi:10.1007/s00209-014-1343-1

A uniqueness theorem for functions in the extended Selberg class

Steven M Gonek, Haseo Ki + Show 1 more

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

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Publication Date: Jun 28, 2014

Citations: 14

Affiliation: Yonsei University, Korea Institute for Advanced Study, Seoul National University

#Extended Selberg Class #Uniqueness Theorem For Functions + Show 8 more

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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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