On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

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

Résumé

Let P (X) ∈ 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 ≥ n 1+c _P .
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Dates et versions

hal-03951306 , version 1 (23-01-2023)
hal-03951306 , version 2 (02-02-2024)

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Citer

Cécile Dartyge, James Maynard. On the largest prime factor of quartic polynomial values: the cyclic and dihedral cases. 2022. ⟨hal-03951306v1⟩

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