On the square-free values of the polynomial \(x^2 + y^2 + z^2 + k\)

DOI10.1016/j.jnt.2021.07.022zbMath1490.11096OpenAlexW3195865108WikidataQ114156786 ScholiaQ114156786MaRDI QIDQ2116757

Guang-Liang Zhou, Yuchen Ding

Publication date: 18 March 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2021.07.022

zbMATH Keywords

Salié sumsquare-free numbers

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Gauss and Kloosterman sums; generalizations (11L05) Estimates on character sums (11L40)

Related Items (3)

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 \(x^2+y^2+z+1\) ⋮ 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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• A New Application of the Hardy-Littlewood-Kloosterman Method
• 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
• Power‐free values of polynomials
• NOTE ON AN ASYMPTOTIC FORMULA CONNECTED WITH r-FREE INTEGERS
• On the frequency of pairs of square-free numbers with a given difference
• Almost-primes represented by quadratic polynomials

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