The modular properties and the integral representations of the multiple elliptic gamma functions
By Atsushi Narukawa. 2003
122 citations recorded by the source corpus.
Abstract We show the modular properties of the multiple “elliptic” gamma functions, which are an extension of those of the theta function and the elliptic gamma function. The modular property of the theta function is known as Jacobi's transformation, and that of the elliptic gamma function was provided by Felder and Varchenko. In this paper, we deal with the multiple sine functions, since the modular properties of the multiple elliptic gamma functions result from the equivalence between two ways to represent the multiple sine functions as infinite products. We also derive integral representations of the multiple sine functions and the multiple elliptic gamma functions. We introduce correspondences between the multiple elliptic gamma functions and the multiple sine functions.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a1fcf0ce0398b90aef3690858db30f6c60e8a2fe
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In Algebra and Number Theory
- V. Spiridonov
- E. Rains
- G. Vartanov
- Eric M. Rains
- S. Ole Warnaar
- A. Selberg
- Peter J. Forrester
- Hjalmar Rosengren
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Limits of elliptic hypergeometric integrals (2006, background): “, ωr) r−1 , where Sr is the multiple sine function (see, for instance, [12]), and Γ (2) h (x; ω1, ω2) = G(−ω1 √ −1,−ω2 √ −1; x − ω1/2 − ω2/2) in terms of Ruijsenaars’ hyperbolic gamma function [18].”
- Essays on the theory of elliptic hypergeometric functions (2008, background): “In [27] there were obtained also infinite product representations of these functions analogous to (2.”