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

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

2010-07-02

arxiv.org/abs/1007.0353v2

Mathematics

Number Theory

Scientific paper

It is not difficult to find an asymptotic formula for the number of pairs of
positive integers $x, y \le H$ 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.

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