Vinogradov's mean value theorem via efficient congruencing

Details Vinogradov's mean value theorem via efficient congruencing Vinogradov's mean value theorem via efficient congruencing

2011-01-03

arxiv.org/abs/1101.0574v1

Mathematics

Number Theory

Scientific paper

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-3.

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