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arXiv · 1801.00210

A study of elliptic gamma function and allies

Vicenţiu Paşol·Wadim Zudilin
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Abstract

We study analytic and arithmetic properties of the elliptic gamma function $$ \prod_{m,n=0}^\infty\frac{1-x^{-1}q^{m+1}p^{n+1}}{1-xq^mp^n}, \qquad |q|,|p|<1, $$ in the regime $p=q$; in particular, its connection with the elliptic dilogarithm and a formula of S. Bloch. We further extend the results to more general products by linking them to non-holomorphic Eistenstein series and, via some formulae of D. Zagier, to elliptic polylogarithms.

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Vicenţiu Paşol, Wadim Zudilin. 2017-12-30. A study of elliptic gamma function and allies. https://doi.org/10.1007/s40687-018-0158-9

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