The largest prime factor of X³+2

2014/11/28 by A. J. Irving, Irving, A. J. · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1412.0024

openalex publication_date 2014/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values \n³+2:n∈ (X,2X]\ have a prime factor larger than X^1+10^-52.

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• The distribution of intersections in SL(3, ℤ) \backslash SL(3, ℝ) and lattices related to roots of cubic congruences

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