A study of elliptic gamma function and allies

Vicenţiu Paşol; Wadim Zudilin

doi:10.1007/s40687-018-0158-9

paper

A study of elliptic gamma function and allies

arXiv:1801.00210 · doi:10.1007/s40687-018-0158-9

Abstract

We study analytic and arithmetic properties of the elliptic gamma function $m, n = 0 \prod \infty \frac{1 - x ^{- 1} q ^{m + 1} p ^{n + 1}}{1 - x q ^{m} p ^{n}}, ∣ q ∣, ∣ p ∣ < 1,$ 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.

12 pages

A study of elliptic gamma function and allies

Abstract

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