Near-optimal mean value estimates for multidimensional Weyl sums

Parsell, Scott T. and Prendiville, Sean and Wooley, Trevor D. (2013) Near-optimal mean value estimates for multidimensional Weyl sums. Geom. Funct. Anal., 23 (6). 1962–2024.

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Abstract

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Item Type:
Journal Article
Journal or Publication Title:
Geom. Funct. Anal.
ID Code:
137149
Deposited By:
Deposited On:
01 Oct 2019 08:10
Refereed?:
Yes
Published?:
Published
Last Modified:
08 Jul 2020 08:59