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

DOI10.1007/s00605-010-0246-4zbMath1297.11118arXiv1007.0353OpenAlexW2044622952MaRDI QIDQ766210

Doychin I. Tolev

Publication date: 23 March 2012

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1007.0353

zbMATH Keywords

Kloosterman sumssquarefree numbers

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Gauss and Kloosterman sums; generalizations (11L05) Distribution of integers with specified multiplicative constraints (11N25)

Related Items (8)

Counting square-free integers represented by binary quadratic forms of a fixed discriminant ⋮ On the consecutive square-free values of the polynomials \(x_1^2 + \cdots + x_k^2+1\), \(x_1^2 + \cdots + x_k^2+2\) ⋮ Square-free numbers of the form \(x^2+y^2+z^2+z+1\) and \(x^2+y^2+z+1\) ⋮ On the number of pairs of positive integers $x, y \leq H$ such that $x^2+y^2+1$, $x^2+y^2+2$ are square-free ⋮ On the \(k\)-free values of the polynomial \(xy^k + C\) ⋮ Consecutive square-free numbers and square-free primitive roots ⋮ On the square-free values of the polynomial \(x^2 + y^2 + z^2 + k\) ⋮ Consecutive square-free values of the type $x^2+y^2+z^2+k$, $x^2+y^2+z^2+k+1$

Cites Work

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• On the power-free values of polynomials in two variables. II
• Powerfree values of binary forms
• Squarefree values of multivariable polynomials
• Einige Sätze über quadratfreie Zahlen
• A New Application of the Hardy-Littlewood-Kloosterman Method
• ON THE EXPONENTIAL SUM WITH SQUARE-FREE NUMBERS
• POWER-FREE VALUES OF BINARY FORMS

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