The Asymptotic Formula in Waring's Problem

Trevor D. Wooley

doi:10.1093/imrn/rnr074

The Asymptotic Formula in Waring's Problem

Trevor D. Wooley^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

46 Citations (Scopus)

Abstract

We derive a new minor arc bound, suitable for applications associated with Waring's problem, from Vinogradov's mean value theorem. In this way, the conjectured asymptotic formula in Waring's problem is established for sums of s kth powers of natural numbers when k >= 6 and s >= 2k(2)-11.

Original language	English
Pages (from-to)	1485-1504
Number of pages	20
Journal	International Mathematics Research Notices
Issue number	7
DOIs	https://doi.org/10.1093/imrn/rnr074
Publication status	Published - 2012

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The Asymptotic Formula in Waring's Problem

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