(2019.07.19 10:30am N224)Frederic Chyzak:Becker's conjecture on k-regular Mahler functions

Time:2019-07-17  Source:

Title                 Becker's conjecture on k-regular Mahler functions

Speaker           Frederic Chyzak (INRIA, Paris, France)

Time&Venue   2019.07.19  10:30am  N224

Abstract:          In 1994, Becker conjectured that if $F(z)$ is a $k$-regular power series, then there exists a $k$-regular rational function $R(z)$such that $F(z)/R(z)$ satisfies a Mahler-type functional equation with polynomial coefficients where the initial coefficient satisfies $a_0(z) = 1$. In this work, we prove Becker’s conjecture in the best possible form; we show that the rational function$R(z)$ can be taken to be a polynomial $z^γ Q(z)$ for some explicit non-negative integer $γ$ and such that $1/Q(z)$ is$k$-regular.

This is joint work with Jason P. Bell, Michael Coons, and Philippe Dumas.