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

Nobushige Kurokawa, Masato Wakayama

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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
Issue number1-2
Publication statusPublished - Mar 2005

All Science Journal Classification (ASJC) codes

  • Applied Mathematics


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