We prove a noncommutative generalisation of Mahler's theorem on interpolation series, a celebrated result of $p$-adic analysis. Mahler's original result states that a function from $\mathbb{N}$ to $\mathbb{Z}$ is uniformly continuous for the $p$-adic metric if and only if it can be uniformly approximated by polynomial functions. We prove an analogous result for functions from a free monoid to a free group, where the $p$-adic metric is replaced by the pro-$p$ metric.

This is Joint work with Christophe Reutenauer.

## Date and Venue

Start Date

Venue

Online Zoom meeting

End Date

## Speaker

Jean-Eric Pin

## Speaker's Institution

IRIF, CNRS

## Files

Jean-Eric Pin-12Feb2021.pdf412.33 KB

## Area

Semigroups, Automata and Languages