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I foresee that to experts of automorphic forms this question will sound unimportant or useless or even not worthy of an answer; but none of these are going to stop me from asking it! The question is ...

In this article, the authors interpret a certain special function, the elliptic Gamma function, defined as $$ \Gamma(z,\tau,\sigma)=\prod_{j,k=0}^\infty\frac{1-e^{2\pi i((j+1)\tau+(k+1)\sigma-z)}}{1-...