Section: New Results
Becker's conjecture on Mahler functions
In 1994, Becker conjectured that if is a -regular power series, then there exists a -regular rational function such that satisfies a Mahler-type functional equation with polynomial coefficients, whose trailing coefficient (i.e., of order 0) is 1. In [2], Frédéric Chyzak and Philippe Dumas, together with Jason P. Bell (University of Waterloo, Canada) and Michael Coons (University of Newcastle, Australia) have proved Becker’s conjecture in the best-possible form: they have shown that the rational function can be taken to be a polynomial for some explicit non-negative integer and such that is -regular. The article was published this year.