Multiple elliptic gamma functions associated to cones
Abstract
We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, associated to good rational cones. We explain how good cones are related to collections of $SL_r(\mathbb{Z})$elements and prove that the generalized multiple sine and multiple elliptic gamma functions enjoy infinite product representations and modular properties determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko, and the results about the usual multiple sine and elliptic gamma functions found by Narukawa.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 arXiv:
 arXiv:1609.02384
 Bibcode:
 2016arXiv160902384W
 Keywords:

 Mathematics  Classical Analysis and ODEs;
 High Energy Physics  Theory
 EPrint:
 27 pages