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Multiple sine functions. (English) Zbl 1065.11065
This paper is an English version of a part of some lecture notes by N. Kurokawa from 1991, the notes having been taken by S. Koyama. In the paper, a theory of multiple sine functions is constructed which generalizes the usual sine function. The double sine function was introduced by Hölder in 1886, and the authors introduce the triple and higher sine functions, studying then their properties, as periodicity, their special values, and algebraic differential equations they satisfy. After this general study, the paper presents an application to the explicit calculation of gamma factors of Selberg zeta functions in terms of Barnes’ multiple gamma functions.

11M36 Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas)
11M35 Hurwitz and Lerch zeta functions
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