A joint universality theorem for periodic Hurwitz zeta-functions. II.
type: Item
instance of: scholarly article
title: A joint universality theorem for periodic Hurwitz zeta-functions. II.
zbMATH Open document ID: 1278.11085
author: S. Skerstonaitė
author: Antanas Laurinčikas
published in: Lithuanian Mathematical Journal
publication date: 2009-11-06T00:00:00Z
review text: The aim of this paper is to prove a joint universality theorem for the functions \(\zeta(s, \alpha_1; \mathfrak A_1), \ldots,\) \(\zeta(s, \alpha_r; \mathfrak A_r)\) without using the hypothesis on the rank of the matrix \(A\) [\textit{A. Javtokas} and the first author [Bull. Aust. Math. Soc. 78, No. 1, 13--33 (2008; Zbl 1228.11136)]. Let \[ L(\alpha_1, \ldots, \alpha_r) =\{\log(m + \alpha_j ): j = 1, \ldots, r, m\in\mathbb N_0.\} \] Theorem. Suppose that the set \(L(\alpha_1, \ldots, \alpha_r)\) is linearly independent over \(\mathbb Q\). Then the functions \(\zeta(s, \alpha_1; \mathfrak A_1), \ldots, \zeta(s, \alpha_r; \mathfrak A_r)\) are universal. The authors note that the linear independence of \(L(\alpha_1, \ldots, \alpha_r)\) holds whenever the numbers \(\alpha_1, \ldots, \alpha_r\) are algebraically independent over \(\mathbb Q\). Therefore, the hypothesis on the numbers \(\alpha_1, \ldots, \alpha_r\) in the present Theorem is weaker than that of the preceding paper (loc. cit.).
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 11M41
zbMATH DE Number: 5626714
zbMATH Keywords: limit theorem
zbMATH Keywords: periodic Hurwitz zeta-function
zbMATH Keywords: probability measure
zbMATH Keywords: universality
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
full work available at URL: s10986-009-9055-7
OpenAlex ID: W2074034993
cites work: Q5560061
cites work: Q3430803
cites work: Universality of the periodic Hurwitz zeta-function
cites work: A JOINT UNIVERSALITY THEOREM FOR PERIODIC HURWITZ ZETA-FUNCTIONS
cites work: The joint universality for periodic Hurwitz zeta-functions
cites work: О функциональной независимости L-функций Дирихле
cites work: Q3292706
DOI: 10.1007/S10986-009-9055-7
description: scientific article; zbMATH DE number 5626714