# A study of elliptic gamma function and allies

@article{Pasol2018ASO, title={A study of elliptic gamma function and allies}, author={Vicentiu Pasol and Wadim Zudilin}, journal={Research in the Mathematical Sciences}, year={2018}, volume={5}, pages={1-11} }

We study analytic and arithmetic properties of the elliptic gamma function $$\begin{aligned} \prod _{m,n=0}^\infty \frac{1-x^{-1}q^{m+1}p^{n+1}}{1-xq^mp^n}, \quad |q|,|p|<1, \end{aligned}$$∏m,n=0∞1-x-1qm+1pn+11-xqmpn,|q|,|p|<1,in the regime $$p=q$$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 Eisenstein series and, via some formulae of D. Zagier, to elliptic…

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