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

Abstract : 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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https://hal.archives-ouvertes.fr/hal-00021542
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Submitted on : Wednesday, March 22, 2006 - 3:12:20 PM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM

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Lucia Di Vizio. Introduction to p-adic q-difference equations (weak Frobenius structure and transfer theorems). 2003. ⟨hal-00021542⟩

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