On the number of pairs of positive integers $x, y \le H$ such that $x^2 + y^2 + 1$ is squarefree

Doychin Tolev

paper

On the number of pairs of positive integers $x, y \leq H$ such that $x^{2} + y^{2} + 1$ is squarefree

arXiv:1007.0353

Abstract

It is not difficult to find an asymptotic formula for the number of pairs of positive integers $x, y \leq H$ such that $x^{2} + y^{2} + 1$ is squarefree. In the present paper we improve the estimate for the error term in this formula using the properties of certain exponential sums. A.Weils's estimate for the Kloosterman sum plays the major role in our analysis.

Cited by in corpus (1)

Errata and Addenda to Mathematical Constants

On the number of pairs of positive integers x,y≤H such that x2+y2+1 is squarefree

Abstract

Cited by in corpus (1)

On the number of pairs of positive integers $x, y \leq H$ such that $x^{2} + y^{2} + 1$ is squarefree