Squarefree polynomials with missing digits

Naomi Bazlov

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arXiv · 2608.17892

Squarefree polynomials with missing digits

Naomi Bazlov

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Abstract

We establish an asymptotic formula for squarefree polynomials over a finite field whose coefficients are in $\{0,1\}$. This resolves a function-field analogue of a conjecture of Erd\H{o}s, Mauduit and S\'ark\"ozy. More generally, we estimate the probability of a polynomial $\sum \varepsilon_it^i$ being squarefree, where $\varepsilon_i$ are random variables sampled according to measures on $\mathbb{F}_q$.

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Naomi Bazlov. 2026-08-18. Squarefree polynomials with missing digits. https://arxiv.org/abs/2608.17892

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