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On the Squarefree Values of $A^4+b^3$ by Sanjaya, Gian Cordana; Wang, Xiaoheng is a scholarly article available to read on EtoBox.

What is On the Squarefree Values of $A^4+b^3$ about?

In this article, we prove that the density of integers $a, b$ such that $a^4+b^3$ 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 $\beta a^4 + \alpha b^3$ for any fixed integers $\alpha$ and $\beta$. We give an exact count for the number of pairs $(a,b)$ of integers with $\max\{|a|^{1/3},|b|^{1/4}\}<X$ such that $\beta a^4 + \alpha b^3$ is squarefree, with a power-saving error term.

Author

Sanjaya, Gian Cordana; Wang, Xiaoheng

Published

2021

Language

EN