Riemann surface of the Riemann zeta function

In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex 1-dimensional, customly denoted as s, another two are complex infinite dimensional, we denote them as b={bn}n=1∞ and z={zn}n=1∞. When b={1}n=1∞ and z={1n}n=1∞ one gets the usual Riem...

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Vydáno v:	Journal of mathematical analysis and applications Ročník 529; číslo 2; s. 126756
Hlavní autor:	Ivashkovich, S.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier Inc 15.01.2024 Elsevier
Témata:	Analytic continuation Mathematics Riemann zeta function Riemann zeta function Analytic continuation
ISSN:	0022-247X, 1096-0813
On-line přístup:	Získat plný text
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Popis
Shrnutí:	In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex 1-dimensional, customly denoted as s, another two are complex infinite dimensional, we denote them as b={bn}n=1∞ and z={zn}n=1∞. When b={1}n=1∞ and z={1n}n=1∞ one gets the usual Riemann zeta function. Our goal in this paper is to study the meromorphic continuation of ζ(b,z,s) as a function of the triple (b,z,s).
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2022.126756