On the squarefree values of a⁴+b³

2021/07/21 by Sanjaya, Gian Cordana, Wang, Xiaoheng · 2 citations
#11N32 #11N36 #11N45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2107.10380

Abstract

In this article, we prove that the density of integers a, b such that a⁴+b³ is squarefree, when ordered by max\|a|^1/3,|b|^1/4\, equals the conjectured product of the local densities. We show that the same is true for polynomials of the form βa⁴ + αb³ for any fixed integers α and β. We give an exact count for the number of pairs (a,b) of integers with max\|a|^1/3,|b|^1/4\

Cited by

• Manin's conjecture for M-points
• Density of Special Classes of Polynomials with Squarefree Discriminant

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• Density of Special Classes of Polynomials with Squarefree Discriminant