Sums of almost equal prime squares
type: Item
instance of: scholarly article
title: Sums of almost equal prime squares
zbMATH Open document ID: 1231.11121
author: Hongze Li
author: Jie Wu
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2009-10-26T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1229624651
review text: It is shown that almost all integers \(n\) satisfying the obvious congruence restrictions can be written as the sum of 3 resp. 4 squares of prime numbers \(p_i\), which have a distance not larger than \(n^{1/2-9/80+\varepsilon}\). The proof uses the circle method. The estimation of the minor arcs uses standard techniques. However, the treatment of the major arcs is more difficult. Although the computations begin as one would expect, approximating the exponential sum over primes by the exponential sum over all integers introduces several difficult error terms, and the main part of the paper is dedicated to the estimation of these terms.
reviewed by: Jan-Christoph Schlage-Puchta
Mathematics Subject Classification ID: 11P32
Mathematics Subject Classification ID: 11P05
Mathematics Subject Classification ID: 11P55
Mathematics Subject Classification ID: 11L20
Mathematics Subject Classification ID: 11L07
zbMATH DE Number: 5620968
zbMATH Keywords: circle method
zbMATH Keywords: sum of prime squares
MaRDI profile type: Publication
OpenAlex ID: W2014408762
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DOI: 10.7169/FACM/1229624651
description: scientific article; zbMATH DE number 5620968