Product Sets of Arithmetic Progressions in Function Fields

We study product sets of finite arithmetic progressions of polynomials over a finite field. We prove a lower bound for the size of the product set, uniform in a wide range of parameters. We apply our results to resolve the function field variants of Erd\H{o}s' multiplication table problem.Comment: We expanded the Literature on Theorem 2.2 and Theorem 2.5 + plus minor revision