Abstract

Recent work in the field of difference equations over the field of rational functions C(x) shows that if a formal power series f is a solution of two linear homogenous difference equations with polynomial coefficients, associated to two "independent" difference operators, then the power series is already a rational function. Last year, a remarkable strengthening of this result was found by Adamczewski, Dreyfus, Hardouin and Wibmer. We report on our work on the same problem over elliptic function fields. Despite the formal similarity, completely new issues arise, having to do (a) with questions of periodicity (b) surprisingly, with the classification of vector bundles on elliptic curves.

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