PreprintCC BY-NC-ND 4.0arXiv
Squarefree Values of Random Polynomials
Abstract
In this paper we consider the error term in the expected count of squarefree values of a polynomial when evaluated at integers n≤ 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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BibTeX
@misc{kerr2026squarefree,
title = {{Squarefree Values of Random Polynomials}},
author = {Bryce Kerr and Watcharakiete Wongcharoenbhorn},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33628},
eprint = {2610.33628},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33628},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Squarefree Values of Random Polynomials
AU - Bryce Kerr
AU - Watcharakiete Wongcharoenbhorn
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33628
UR - https://arxiv.org/abs/2610.33628
AB - In this paper we consider the error term in the expected count of squarefree values of a polynomial when evaluated at integers n≤ 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
ER -