On Waring's problem (elementary methods)
type: Item
instance of: scholarly article
title: On Waring's problem (elementary methods)
zbMATH Open document ID: 1072.11073
author: Yuri V. Nesterenko
published in: Journal of Mathematical Sciences (New York)
publication date: 2005-07-14T00:00:00Z
full work available at URL: https://eudml.org/doc/227565
review text: The problem in the title is to prove that for each integer \(n > 1\) there is an integer \(m > 1\) such that every integer \(N > 1\) is a sum of at most \(m\) positive \(n\)-powers. After the problem was solved for small values of \(n,\) Hilbert solved it in general. His proof uses integration. The paper reviews and simplifies proofs which do not use integration. The paper does not refer to connections with spherical designs and isometric embeddings of Banach spaces [cf., e.g., \textit{Y. I. Lyubich} and \textit{L. N. Vaserstein}, Geom. Dedicata 47, No. 3, 327--362 (1993; Zbl 0785.52002)].
Mathematics Subject Classification ID: 11P05
zbMATH DE Number: 2187244
zbMATH Keywords: Waring problem
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
OpenAlex ID: W2083870926
cites work: Q4163296
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cites work: On the additive properties of numbers
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cites work: Large improvements in Waring's problem
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DOI: 10.1007/S10958-006-0266-8
description: scientific article; zbMATH DE number 2187244