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.
Information
Published: 1 January 2020
First available in Project Euclid: 27 May 2020
zbMATH: 07283182
Digital Object Identifier: 10.2969/aspm/08410079
Subjects:
Primary:
11M35
Keywords:
Derivative of Lerch zeta-function
,
trivial and nontrivial zeros
,
zero-free regions
Rights: Copyright © 2020 Mathematical Society of Japan
