On the periodic Hurwitz zeta-function.

Abstract

International audience In this paper, an universality theorem in the Voronin sense for the periodic Hurwitz zeta-function is proved.

Remarks on the Mixed Joint Universality for A class of Zeta Functions

“…Let B = {b m : m ∈ N 0 } be a periodic sequence of complex numbers (not all zero) with minimal period k ∈ N, and 0 < α ≤ 1. In 2006, A. Javtokas and A. Laurinčikas [3] introduced the periodic Hurwitz zeta-function ζ (s, α; B). For σ > 1, it is given by the series…”

“…Next we need an approximation lemma in the mean value sense, similar to [5, Lemma 3.3]. In the proof of [5, Lemma 3.3], we used the result of [3]. The desired approximation can be shown by using, instead of [3], mean value results given in [10, (2.3), (2.5)].…”

“…In the proof of [5, Lemma 3.3], we used the result of [3]. The desired approximation can be shown by using, instead of [3], mean value results given in [10, (2.3), (2.5)].…”

On mixed joint discrete universality for a class of zeta-functions. II

“…Now we recall the definition of the periodic Hurwitz zeta-function ζ (s, α; B) with a fixed parameter α, 0 < α ≤ 1. (Remark: The function ζ (s, α; B) was introduced by A. Javtokas and A. Laurinčikas in [8].) Let B = {b m : m ∈ N 0 } be a periodic sequence of complex numbers (not all zero) with minimal period k ∈ N. For σ > 1, the function ζ (s, α; B) is defined by…”

A SURVEY ON THE THEORY OF UNIVERSALITY FOR ZETA AND L-FUNCTIONS

“…This result is a consequence of the hybrid joint universality theorem of Kaczorowski and Kulas [61] (see Section 15). Javtokas and Laurinčikas [49] [50] studied the strong universality for periodic Hurwitz zeta-function…”