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 language | English |
|---|---|
| Pages (from-to) | 179-201 |
| Number of pages | 23 |
| Journal | Acta Applicandae Mathematicae |
| Volume | 86 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - Mar 1 2005 |
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All Science Journal Classification (ASJC) codes
- Applied Mathematics
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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 journal › Article
}
TY - JOUR
T1 - Extensions of zeta functions - Examples and a study of the double sine functions
AU - Kurokawa, Nobushige
AU - Wakayama, Masato
PY - 2005/3/1
Y1 - 2005/3/1
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
VL - 86
SP - 179
EP - 201
JO - Acta Applicandae Mathematicae
JF - Acta Applicandae Mathematicae
SN - 0167-8019
IS - 1-2
ER -