Product Sets of Arithmetic Progressions in Function Fields
Number Theory
2023-09-19 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2309.05046,
title = {Product Sets of Arithmetic Progressions in Function Fields},
author = {Lior Bary-Soroker and Noam Goldgraber},
journal= {arXiv preprint arXiv:2309.05046},
year = {2023}
}
Comments
We expanded the Literature on Theorem 2.2 and Theorem 2.5 + plus minor revisions