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arXiv · 1605.07765

On square-free values of large polynomials over the rational function field

Dan Carmon·Alexei Entin
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Abstract

We investigate the density of square-free values of polynomials with large coefficients over the rational function field $\mathbb{F}_q[t]$. Some interesting questions answered as special cases of our results include the density of square-free polynomials in short intervals, and an asymptotic for the number of representations of a large polynomial $N$ as a sum of a small $k$-th power and a square-free polynomial.

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Dan Carmon, Alexei Entin. 2016-05-25. On square-free values of large polynomials over the rational function field. https://arxiv.org/abs/1605.07765

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