A note on sums of five almost equal prime squares
type: Item
instance of: scholarly article
title: A note on sums of five almost equal prime squares
zbMATH Open document ID: 0886.11059
author: C. Bauer
published in: Archiv der Mathematik
publication date: 1997-11-11T00:00:00Z
review text: \textit{L. K. Hua} proved in [Q. J. Math., Oxf. Ser. 9, 68-80 (1938; Zbl 0018.29404)] that every sufficiently large integer \(N\equiv 5\pmod{24}\) is the sum of five prime squares. In this paper, the author shows that these primes can be restricted to short intervals of the form \([\sqrt{N/5}- U,\sqrt{N/5}+ U]\), where \(U= N^{9/20+\varepsilon}\) under the GRH and \(U= N^{1/2-\delta}\) unconditionally. The proof of this result uses the circle method and follows the techniques developed in two previous papers by \textit{M. C. Liu} and \textit{K. M. Tsang} [Monatsh. Math. 111, 147-169 (1991; Zbl 0719.11064) and in Théorie des nombres, C. R. Conf. Int., Quebec/Can. 1987, 595-624 (1989; Zbl 0682.10043)]. On the minor arcs, the contribution is bounded by an estimation for the exponential sum \(\sum_{x<n\leq x+y}\Lambda(n)e(n^2\alpha)\) given by \textit{J. Y. Liu} and \textit{T. Zhan} [Acta Arith. 77, 369-383 (1996; Zbl 0863.11067)].
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 11L07
Mathematics Subject Classification ID: 11P55
zbMATH DE Number: 1052892
zbMATH Keywords: primes in short intervals
zbMATH Keywords: sum of five prime squares
zbMATH Keywords: circle method
reviewed by: Kai-Man Tsang
MaRDI profile type: Publication
full work available at URL: s000130050089
OpenAlex ID: W2156421370
DOI: 10.1007/S000130050089
description: scientific article; zbMATH DE number 1052892