An asymptotic formula related to the divisors of the quaternary quadratic form
type: Item
instance of: scholarly article
title: An asymptotic formula related to the divisors of the quaternary quadratic form
zbMATH Open document ID: 1329.11105
author: Liqun Hu
published in: Acta Arithmetica
publication date: 2014-11-07T00:00:00Z
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11P55
zbMATH DE Number: 6366984
zbMATH Keywords: circle method
zbMATH Keywords: divisor problem
zbMATH Keywords: quadratic form
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4064/aa166-2-2
OpenAlex ID: W2320133013
cites work: On divisors of a quadratic form
cites work: Hyperbolic prime number theorem
cites work: On the Number of Divisors of the Quadratic Form m2 + n2
DOI: 10.4064/AA166-2-2
review text: Let \(d(n)\) and \(\Lambda(n)\) stand for the divisor function and the Mangoldt function. This paper gives an asymptotic formula for the following sums: NEWLINE\[NEWLINE\begin{aligned}& \sum\limits_{m_{i}\leq x}d(m^{2}_{1}+m^{2}_{2}+m^{2}_{3}+m^{2}_{4}), \\ &\sum\limits_{m_{i}\leq x}\Lambda(m^{2}_{1}+m^{2}_{2}+m^{2}_{3}+m^{2}_{4}).\end{aligned}NEWLINE\]NEWLINE The proof uses the circle method.
reviewed by: Zaizhao Meng
description: scientific article; zbMATH DE number 6366984