Average behavior of the triple divisor function over values of quadratic form
type: Item
instance of: scholarly article
title: Average behavior of the triple divisor function over values of quadratic form
zbMATH Open document ID: 1478.11057
author: Guangwei Hu
author: Weiwei Hu
published in: Lithuanian Mathematical Journal
publication date: 2021-07-07T00:00:00Z
review text: Let \(d_3(n)\) denote the number of representations of \(n\) as the product of \(3\) natural numbers. The authors prove asymptotic formulas for this triple divisor function over values of a quadratic form \(n^2_1+\cdots+ n^2_l\) with \(l\ge 3\), i.e., for \(\sum_{1\le n_1,\dots, n_l\le \sqrt{x}} d_3(n^2_1+\cdots+ n^2_l)\). The proof uses the circle method.
Mathematics Subject Classification ID: 11E25
Mathematics Subject Classification ID: 11P55
zbMATH DE Number: 7369419
zbMATH Keywords: triple divisor function
zbMATH Keywords: circle method
reviewed by: Meinhard Peters
MaRDI profile type: Publication
full work available at URL: s10986-020-09500-x
OpenAlex ID: W3096180949
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DOI: 10.1007/S10986-020-09500-X
description: scientific article; zbMATH DE number 7369419