TY - JOUR
T1 - Extensions of zeta functions - Examples and a study of the double sine functions
AU - Kurokawa, Nobushige
AU - Wakayama, Masato
N1 - Funding Information:
★ Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012, and by Grant-in-Aid for Exploratory Research No. 13874004. This is based on the talk at “The 2002 Twente Conference on Lie Groups” 16–18 Dec. University of Twente, Enschede, The Netherlands.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005/3
Y1 - 2005/3
N2 - 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.
AB - 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.
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U2 - 10.1007/s10440-005-0469-x
DO - 10.1007/s10440-005-0469-x
M3 - Article
AN - SCOPUS:17444423709
VL - 86
SP - 179
EP - 201
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
SN - 0167-8019
IS - 1-2
ER -