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October 2020 The Density Function for the Value-Distribution of the Lerch Zeta-Function and Its Applications
Masahiro Mine
Michigan Math. J. 69(4): 849-889 (October 2020). DOI: 10.1307/mmj/1586570481

Abstract

The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure related to the value-distribution of the Lerch zeta-function. We prove that it has a density function, and we can explicitly construct it. Moreover, we prove an asymptotic formula for the number of zeros of the Lerch zeta-function on the right side of the critical line, whose main term is associated with the density function.

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Masahiro Mine. "The Density Function for the Value-Distribution of the Lerch Zeta-Function and Its Applications." Michigan Math. J. 69 (4) 849 - 889, October 2020. https://doi.org/10.1307/mmj/1586570481

Information

Received: 3 December 2018; Revised: 13 September 2019; Published: October 2020
First available in Project Euclid: 11 April 2020

MathSciNet: MR4168789
Digital Object Identifier: 10.1307/mmj/1586570481

Subjects:
Primary: 11M35
Secondary: 11J68

Rights: Copyright © 2020 The University of Michigan

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Vol.69 • No. 4 • October 2020
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