Bilateral zeta functions associated with the multiple sine functions

2014/09/07 by Genki Shibukawa, Shibukawa, Genki
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #math.CA #msc:11M06 #msc:11M35 #msc:33E20

paper · pdf · doi:10.48550/arxiv.1409.2074

17 pages, no figures

arxiv created 2014/09/07 · arxiv updated 2014/09/09

Abstract

We introduce two types bilateral zeta functions, which are related to the primitive and normalized multiple sine functions respectively. Further, we establish their main properties, that is, Fourier expansions, analytic continuations, differential and difference equations, special values. By applying these results, we obtain not only some generalization of the primitive and normalized multiple sine functions but also simple construction of the multiple sine function theory.

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