Vinogradov's mean value theorem via efficient congruencing
Author:
- Trevor WooleyTWTrevor Wooley
- 1 May 2012
- journal article
- Published by Annals of Mathematics in Annals of Mathematics
- Vol. 175 (3) , 1575-1627
Abstract
We obtain estimates for Vinogradov's integral which for the first time approach those conjectured to be the best possible. Several applications of these new bounds are provided. In particular, the conjectured asymptotic formula in Waring's problem holds for sums of s kth powers of natural numbers whenever s is at least 2k^2+2k-3Keywords
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