Vol. 10, No. 2, 2021
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Joint universality and simple $a$-points of Lerch zeta-functions

Hirofumi Nagoshi
Vol. 10 (2021), No. 2, 121–139
DOI: 10.2140/moscow.2021.10.121
Abstract

For 0 < α ≤ 1 and 0 < λ ≤ 1, let L(s,α,λ) denote the associated Lerch zeta-function, which is defined to be ∑ n=0∞e2πinλ(n + α)−s for Res > 1. We obtain the joint universality theorem for the collection of Lerch zeta-functions ⋃ j=1J{L(s,αj,λ) : 0 < λ ≤ 1}, when α1,…,αJ satisfy a certain condition. This theorem is an improvement of several previous joint universality theorems for Lerch zeta-functions. We also investigate the distribution of simple a-points of Lerch zeta-functions and their derivatives.

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Keywords
Lerch zeta-function, joint universality, $a$-point, value-distribution
Mathematical Subject Classification
Primary: 11M35
Milestones
Received: 3 October 2020
Accepted: 1 March 2021
Published: 23 June 2021
Authors
Hirofumi Nagoshi
Faculty of Science and Technology
Gunma University
Kiryu
Japan