English

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

R2 v1 2026-06-28T12:17:23.563Z