q-strong Frobenius structure

Abstract: The notion of strong Frobenius structure is classically studied in the theory of $p$-adic differential equations. This notion was introduced by B.Dwork in his study of zeta functions. Recently, we propose a new definition of this notion for q-difference operators. The relevance of this definition is supported for two results. The first one deals with confluence and the second one deals with congruence modulo the cyclotomic polynomial. So the first part of the talk is devoted to presenting our definition of q-strong Frobenius structure and the second part we are going to present the two previous results.

number theory

Audience: researchers in the topic

Warsaw Number Theory Seminar