Shifted divisor problem and random divisor problem
type: Item
instance of: scholarly article
title: Shifted divisor problem and random divisor problem
zbMATH Open document ID: 0786.11060
author: Masumi Nakajima
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-05-09T00:00:00Z
review text: Let \(\alpha\), \(\beta\) be fixed constants with \(0<\alpha\leq 1\), \(0<\beta\leq 1\). The author considers the lattice point problem \(D(x;\alpha,\beta)= \# \{(m,n)\): \(m,n\in\mathbb{N}\cup\{0\}\), \((m+\alpha) (n+\beta)\leq x\}\), where the points with \((m+\alpha) (n+\beta)=x\) are counted with a factor \(1/2\). It is established a Voronoi-type identity and upper and lower bounds for the error term in the asymptotic expansion of \(D(x;\alpha,\beta)\). There are only short outlines of the proofs.
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 488096
zbMATH Keywords: shifted divisor problem
zbMATH Keywords: lattice point problem
zbMATH Keywords: Voronoi-type identity
zbMATH Keywords: upper and lower bounds
zbMATH Keywords: error term
zbMATH Keywords: asymptotic expansion
reviewed by: Ekkehard Krätzel
MaRDI profile type: Publication
full work available at URL: pjaa.69.49
OpenAlex ID: W1985434683
cites work: Q5621389
cites work: Q3220660
cites work: ON THE NUMBER OF LATTICE POINTS INSIDE A RANDOM OVAL
cites work: ON THE NUMBER OF POINTS OF A GIVEN LATTICE IN A RANDOM HYPERSPHERE
cites work: Q3291025
DOI: 10.3792/PJAA.69.49
description: scientific article; zbMATH DE number 488096