Functional distribution for a collection of Lerch zeta functions
type: Item
instance of: scholarly article
title: Functional distribution for a collection of Lerch zeta functions
zbMATH Open document ID: 1317.11089
author: Hidehiko Mishou
published in: Journal of the Mathematical Society of Japan
publication date: 2015-01-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jmsj/1414090236
review text: Let \(L(\lambda ,\alpha ,s)=\sum _{n=0}^{\infty }\frac{e^{2\pi {\kern 1pt} i\lambda n{\kern 1pt} } }{(n+\alpha )^{s} } \) be the Lerch zeta function. Motivated by some results of \textit{A. Laurinčikas} [Lith. Math. J. 37, No. 3, 275--280 (1997); translation from Liet. Mat. Rink. 37, No. 3, 367--375 (1997; Zbl 0938.11045)], the author formulates here the following conjecture: Let \(0<\alpha <1\) be a transcendental real number and let also \(\lambda _{{\kern 1pt} 1} ,\lambda _{{\kern 1pt} 2} ,\ldots,\lambda _{{\kern 1pt} r} \) be distinct real numbers in the interval \([0,1)\). Then the joint universality theorem holds for the set of Lerch zeta functions \(\left\{L(\lambda _{j} ,\alpha ,s)|1\leq j\leq r\right\}\) on the strip \(1/2<\mathrm{Re} (s)<1\) . \noindent The author presents some results which justify this conjecture. For example, it is proved that the joint universality theorem holds for the set \(\left\{L(\lambda _{j} ,\alpha ,s)\right\}\)for almost all real numbers \(\lambda _{j} \).
reviewed by: Khristo N. Boyadzhiev
Mathematics Subject Classification ID: 11M35
Mathematics Subject Classification ID: 11K38
zbMATH DE Number: 6383637
zbMATH Keywords: Lerch zeta function
zbMATH Keywords: joint universality theorem
MaRDI profile type: Publication
OpenAlex ID: W1965247549
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cites work: The Riemann zeta-function. Transl. from the Russian by Neal Koblitz
DOI: 10.2969/JMSJ/06641105
description: scientific article; zbMATH DE number 6383637