Additive representation in short intervals, II: sums of two like powers

Jörg Brüdern*, Trevor D. Wooley

*Corresponding author for this work

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

176 Downloads (Pure)

Abstract

We establish that, for almost all natural numbers N, there is a sum of two positive integral cubes lying in the interval [NN7/18+ϵ,N]. Here, the exponent 7/18 lies half way between the trivial exponent 4/9 stemming from the greedy algorithm, and the exponent 1/3 constrained by the number of integers not exceeding X that can be represented as the sum of two positive integral cubes. We also provide analogous conclusions for sums of two positive integral k-th powers when k≥4.
Original languageEnglish
Pages (from-to)179-196
Number of pages18
JournalMathematische Zeitschrift
Volume286
Issue number1-2
Early online date13 Oct 2016
DOIs
Publication statusPublished - 8 May 2017

Keywords

  • Sums of cubes
  • sums of k-th powers
  • Hardy-Littlewood method

Fingerprint Dive into the research topics of 'Additive representation in short intervals, II: sums of two like powers'. Together they form a unique fingerprint.

Cite this