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arXiv · 1502.05996

Multiple sine, multiple elliptic gamma functions and rational cones

Luigi Tizzano·Jacob Winding
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Abstract

We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, labelled by rational cones in $\mathbb{R}^r$. For $r=2,3$ we prove that the generalized multiple elliptic gamma functions enjoy a modular property determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko. The generalized multiple sine enjoy a related infinite product representation, generalizing the results of Narukawa for the ordinary multiple sine functions.

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Luigi Tizzano, Jacob Winding. 2014-12-19. Multiple sine, multiple elliptic gamma functions and rational cones. https://arxiv.org/abs/1502.05996

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