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arXiv · 2601.16657

Product representations of polynomials over finite fields

Hyunwoo Lee·Chi Hoi Yip·Semin Yoo
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Abstract

Erdős, Sárközy, and Sós studied the asymptotics of the maximum size of a subset of $\{1,2,\ldots, N\}$ such that it does not contain $k$ distinct elements whose product is a perfect square. More generally, Verstraëte proposed a conjecture regarding the asymptotic behavior of the same quantity with the set of perfect squares replaced by the value set of a polynomial in $\mathbb{Z}[x]$. In this paper, we study a finite field analogue of Verstraëte's conjecture.

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Hyunwoo Lee, Chi Hoi Yip, Semin Yoo. 2026-08-09. Product representations of polynomials over finite fields. https://arxiv.org/abs/2601.16657

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