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Near-optimal mean value estimates for multidimensional Weyl sums

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<mark>Journal publication date</mark>2013
<mark>Journal</mark>Geom. Funct. Anal.
Issue number6
Volume23
Number of pages63
Pages (from-to)1962–2024
Publication StatusPublished
<mark>Original language</mark>English

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.