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arXiv · 2610.33628

Squarefree Values of Random Polynomials

Bryce Kerr·Watcharakiete Wongcharoenbhorn
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Abstract

In this paper we consider the error term in the expected count of squarefree values of a polynomial when evaluated at integers \(n\le N\). We prove a power saving on average over polynomials of fixed degree and height at most \(H\). Our results improve previous estimates of Browning and Shparlinski in that the required range of \(H\) is independent of the degree, but depends on \(N\)

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Bryce Kerr, Watcharakiete Wongcharoenbhorn. 2026-10-24. Squarefree Values of Random Polynomials. https://arxiv.org/abs/2610.33628

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