Properties of continued fractions in the field of p-adic numbersMPIM

by Giuliano Romeo (Charles University Prague)

Tuesday Oct 21, 2025, 11:00 AM → 12:00 PM Europe/Berlin

MPIM, Vivatsgasse, 7 - Lecture Hall (Max Planck Institute for Mathematics)

Number theory lunch seminar

In this talk we provide an overview of the theory of p-adic continued fractions and we discuss the most important algorithms that have been defined throughout the years. We focus in particular on the properties of convergence, finiteness and periodicity, together with the most recent developments towards the proof a p-adic version of Lagrange's Theorem. In the last part of the talk, we present some results on their arithmetic and an analogue of Gosper's algorithm for computing the Möbius trasnform of p-adic continued fractions.