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

DOI10.4064/aa190118-25-7zbMath1469.11263arXiv1901.04838OpenAlexW3009945430MaRDI QIDQ3298864

Stoyan Ivanov Dimitrov

Publication date: 16 July 2020

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.04838

zbMATH Keywords

Gauss sumsasymptotic formulasquare-free 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 (7)

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 \(x^2+y^2+z+1\) ⋮ Pairs of square-free values of the type $n^2+1$, $n^2+2$ ⋮ 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 number of pairs of positive integers \(x,y \leq H\) such that \(x^2+y^2+1\) is squarefree
• The square sieve and consecutive square-free numbers
• A New Application of the Hardy-Littlewood-Kloosterman Method
• ON THE EXPONENTIAL SUM WITH SQUARE-FREE NUMBERS
• On the distribution of consecutive square-free numbers of the form $\mathbf{[\alpha n, [\alpha n]+1}$]
• CONSECUTIVE SQUARE-FREE NUMBERS OF THE FORM [nc, [nc] + 1]

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