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Product Sets of Arithmetic Progressions in Function Fields

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arxiv 2309.05046 v2 pith:STQSJ3K4 submitted 2023-09-10 math.NT

Lior Bary-Soroker , Noam Goldgraber This is my paper · ORCID
classification math.NT
keywords productarithmeticfieldfinitefunctionprogressionssetsapply
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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.

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  1. Central limit theorems for random multiplicative functions over function fields

    math.NT 2025-11 conditional novelty 6.0 of 10

    A sufficiently large polynomial set with asymptotically trivial multiplicative energy yields a complex Gaussian limit for Steinhaus random multiplicative sums; short intervals, few prime factors, shifted primes, and r...

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