The arithmetic of power series and applications to irrationality

Abstract: In this talk, we will discuss various irrationality and linear independence problems including certain products of two (classical or p-adic) log values. The proofs use an arithmetic holonomicity theorem, the special case of which was used in the proof of the unbounded denominators conjecture; our arithmetic holonomicity theorem is inspired from Andre’s work on Grothendieck-Katz p-curvature conjecture on arithmetic differential equations. A geometric version of our arithmetic holonomicity theorems have also been studied in recent work of Bost and Charles.

This is joint work in progress with Frank Calegari and Vesselin Dimitrov.

number theory

Audience: researchers in the topic

BC-MIT number theory seminar