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arXiv · 2212.03381

On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases

Cécile Dartyge·James Maynard
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Abstract

Let $P(X)\in\mathbb{Z}[X]$ be an irreducible, monic, quartic polynomial with cyclic or dihedral Galois group. We prove that there exists a constant $c_P>0$ such that for a positive proportion of integers $n$, $P(n)$ has a prime factor $\ge n^{1+c_P}$.

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Cécile Dartyge, James Maynard. 2022-12-07. On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases. https://arxiv.org/abs/2212.03381

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