Elliptic (p,q)-difference modules
arXiv:2007.09508 · doi:10.2140/ant.2021.15.1303
Abstract
We study finite dimensional vector spaces over fields of elliptic functions equipped with two commuting aotomorphisms σand τinduced by isogenies of relatively prime orders. We give a structure theorem for such objects, that reveals a connection to the classification of vector bundles on elliptic curves by Atiyah. As an application we prove an elliptic analogue of a conjecture of Loxton and van der Poorten which has been recently proved by Adamczewski and Bell.
34 pages