Additive representation in short intervals, I: Waring's problems for cubes

J Brüdern, TD Wooley

Research output: Contribution to journalArticle (Academic Journal)peer-review

2 Citations (Scopus)

Abstract

Estimates are established for the number of integers of size N, in intervals of size N-theta, that fail to admit a representation as the sum of s cubes (s = 5, 6). Thereby it is shown that almost all such integers are represented in the proposed manner. When s = 5 one may take theta = 10/21, and when s = 6 one may take any theta > 17/63. Similar such conclusions are also established for the related problem associated with the expected asymptotic formula.
Translated title of the contributionAdditive representation in short intervals, I: Waring's problems for cubes
Original languageEnglish
Pages (from-to)1197 - 1220
Number of pages24
JournalCompositio Mathematica
Volume140 (5)
DOIs
Publication statusPublished - 1 Sep 2004

Bibliographical note

Publisher: London Math Soc

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