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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Veröffentlicht in:Journal of mathematical analysis and applications Jg. 529; H. 2; S. 126756
1. Verfasser: Ivashkovich, S.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.01.2024
Elsevier
Schlagworte:
Analytic continuation
Mathematics
Riemann zeta function
Riemann zeta function
Analytic continuation
ISSN:0022-247X, 1096-0813
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Zusammenfassung: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