Number Theory Seminar: Jason Bell

Let K be a field of characteristic zero and let k and l be two multiplicatively independent positive integers. We prove the following result: a power series F(x) in K[[x]] satisfies both a k- and a l-Mahler type functional equation if and only if it is a rational function. This proves conjecture of Loxton and van der Poorten. This is joint work with Boris Adamczewski.