Extensions of zeta functions - Examples and a study of the double sine functions

Nobushige Kurokawa, Masato Wakayama

Research output: Contribution to journalArticle

Abstract

We discuss zeta extensions in the sense of Kurokawa and Wakayama, Proc. Japan Acad. 2002, for constructing new zeta functions from a given zeta function. This notion appeared when we introduced higher zeta functions such as higher Riemann zeta functions in Kurokawa et al., Kyushu Univ. Preprint, 2003, and a higher Selberg zeta functions in Kurokawa and Wakayama, Comm. Math. Phys., 2004. In this article, we first recall some explicit examples of such zeta extensions and give a conjecture about functional equations satisfied by higher zeta functions. We devote the second part to making a detailed study of the double sine functions which are treated in a framework of the zeta extensions.

Original languageEnglish
Pages (from-to)179-201
Number of pages23
JournalActa Applicandae Mathematicae
Volume86
Issue number1-2
DOIs
Publication statusPublished - Mar 1 2005

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Riemann zeta function
Selberg zeta Function
Japan
Functional equation

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cite this

Extensions of zeta functions - Examples and a study of the double sine functions. / Kurokawa, Nobushige; Wakayama, Masato.

In: Acta Applicandae Mathematicae, Vol. 86, No. 1-2, 01.03.2005, p. 179-201.

Research output: Contribution to journalArticle

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