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Difference equations over fields of elliptic functions.

Banff International Research Station for Mathematical Innovation and Discovery

Adamczewski and Bell proved in 2017 a 30-year old conjecture of Loxton and van der Poorten, asserting that a Laurent power series, which simultaneously satisfies a p-Mahler equation and a q-Mahler equation for multiplicatively independent integers p and q, is a rational function. Similar looking theorems have been proved by Bezivin-Boutabaa and Ramis for pairs of difference, or difference-differential equations. Recently, Schafke and Singer gave a unified treatment of all these theorems. In this talk we shall discuss a similar theorem for (p,q)-difference equations over fields of elliptic functions. Despite having the same flavor, there are substantial differences, having to do with issues of periodicity, and with the existence of non-trivial (p,q)-invariant vector bundles on the elliptic curve.

Mathematics; Dynamical systems and ergodic theory; Difference and functional equations; Dynamical systems

video/mp4

Author affiliation: Hebrew University of Jerusalem

2021-05-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/78217

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/