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

Lucia Di Vizio (1)

1 LEP - Laboratoire Émile Picard

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.

Domaines: Théorie des nombres [math.NT]; Algèbres quantiques [math.QA]

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