A study of elliptic gamma function and allies
Abstract
We study analytic and arithmetic properties of the elliptic gamma function $$ \prod_{m,n=0}^\infty\frac{1x^{1}q^{m+1}p^{n+1}}{1xq^mp^n}, \qquad q,p<1, $$ 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 nonholomorphic Eistenstein series and, via some formulae of D. Zagier, to elliptic polylogarithms.
 Publication:

arXiv eprints
 Pub Date:
 December 2017
 arXiv:
 arXiv:1801.00210
 Bibcode:
 2018arXiv180100210P
 Keywords:

 Mathematics  Number Theory;
 Mathematical Physics;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  KTheory and Homology;
 Primary 33E30;
 Secondary 11F03;
 11G16;
 11G55;
 33E05
 EPrint:
 12 pages