Distribution of lattice points over the four-dimensional sphere
type: Item
instance of: scholarly article
title: Distribution of lattice points over the four-dimensional sphere
zbMATH Open document ID: 1005.11043
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-08-29T00:00:00Z
review text: Let \(r_k(n)\) denote the number of representations of \(n\) by a sum of \(k\) squares of integers. If \(0< A< 1\) is a constant, then it is proved that \[ \sum_{-A\sqrt{n}\leq w\leq A\sqrt{n}} r_3(n-w^2)= \mu_4(A) r_4(n)+ O(n^\alpha), \] where \(\mu_4(A)> 0\). The author improves his former estimation with \(\alpha= \frac{3}{4}+ \varepsilon\) to \(\alpha= \frac{1487} {2000}\). He combines his own method with a method of \textit{E. P. Golubeva} [Zap. Nauchn. Semin. LOMI 144, 27-37 (1985; Zbl 0568.10013)], which was used to estimate some singular series.
reviewed by: Ekkehard Krätzel
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11P21
zbMATH DE Number: 1777285
zbMATH Keywords: asymptotic results on arithmetic functions
zbMATH Keywords: sums of squares
author: Oleg M. Fomenko
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1777285