Advanced Studies in Pure Mathematics

Zeros of derivative of Lerch's zeta-function

Ramūnas Garunkštis, Raivydas Šimėnas, and Rokas Tamošiūnas

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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.

Article information

Source
Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto's 60th birthday, H. Mishou, T. Nakamura, M. Suzuki and Y. Umegaki, eds. (Tokyo: Mathematical Society of Japan, 2020), 79-91

Dates
Received: 23 December 2017
Revised: 15 February 2018
First available in Project Euclid: 27 May 2020

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1590597084

Digital Object Identifier
doi:10.2969/aspm/08410079

Subjects
Primary: 11M35: Hurwitz and Lerch zeta functions

Keywords
Derivative of Lerch zeta-function zero-free regions trivial and nontrivial zeros

Citation

Garunkštis, Ramūnas; Šimėnas, Raivydas; Tamošiūnas, Rokas. Zeros of derivative of Lerch's zeta-function. Various Aspects of Multiple Zeta Functions — in honor of Professor Kohji Matsumoto's 60th birthday, 79--91, Mathematical Society of Japan, Tokyo, Japan, 2020. doi:10.2969/aspm/08410079. https://projecteuclid.org/euclid.aspm/1590597084


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