Zeros of derivative of Lerch's zeta-function

Name: Zeros of derivative of Lerch's zeta-function
Keywords: Derivative of Lerch zeta-function, trivial and nontrivial zeros, zero-free regions, 11M35

Garunkštis, Ramūnas; Šimėnas, Raivydas; Tamošiūnas, Rokas

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Other literature type . 2020

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https://doi.org/10.2969/aspm/0...

Article . 2020 . Peer-reviewed

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https://dx.doi.org/10.2969/asp...

Other literature type

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Zeros of derivative of Lerch's zeta-function

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 27 May 2020Publisher:Mathematical Society of JapanJournal:Advanced Studies in Pure Mathematics (issn: 0920-1971,

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Authors: Garunkštis, Ramūnas; Šimėnas, Raivydas; Tamošiūnas, Rokas;

doi: 10.2969/aspm/08410079

Zeros of derivative of Lerch's zeta-function

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Abstract

In this paper, we study the distribution of the zeros of the derivative of the Lerch zeta-function. We indicate the zero-free regions and the positions of the trivial zeros. Also, we consider an asymptotic formula for the number of nontrivial zeros and show that almost all nontrivial zeros are arbitrarily close to the critical line.

Keywords

Derivative of Lerch zeta-function, trivial and nontrivial zeros, zero-free regions, 11M35

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