Product Sets of Arithmetic Progressions in Function Fields

2023/09/10 by Lior Bary‐Soroker, Noam Goldgraber, Bary-Soroker, Lior +1 · 1 citation
Computer Science · Mathematics · #11N55 (Secondary) #11T06 (primary) #11T55 #Algebraic Geometry and Number Theory #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2309.05046

openalex publication_date 2023/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Erdős' multiplication table problem.

Cited by

• Central limit theorems for random multiplicative functions over function fields

Related

• Erdős' Multiplication Table Problem for Function Fields and Symmetric Groups
• Arithmetic and Geometric Progressions in Productsets over Finite Fields
• On product sets of arithmetic progressions
• Product sets cannot contain long arithmetic progressions
• Improved bounds for arithmetic progressions in product sets