Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems)

Details Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems) Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems)

2002-11-14

arxiv.org/abs/math/0211217v3

Mathematics

Number Theory

59 pages. Refereed version: some inaccuracies have been corrected. To appear in Geometric Aspects of Dwork's Theory (Dwork Tri

Scientific paper

Inspired by the theory of p-adic differential equations, this paper introduces an analogous theory for q-difference equations over a local field, when |q|=1. We define some basic concepts, for instance the generic radius of convergence, introduce technical tools, such as a twisted Taylor formula for analytic functions, and prove some fundamental statements, such as an effective bound theorem, the existence of a weak Frobenius structure and a transfer theorem in regular singular disks.

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