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Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums

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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.

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Correspondence to Trevor D. Wooley.

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S.T. Parsell was supported by National Security Agency Grant H98230-11-1-0190, S.M. Prendiville by an EPSRC doctoral training grant through the University of Bristol, and T.D. Wooley by a Royal Society Wolfson Research Merit Award.

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Parsell, S.T., Prendiville, S.M. & Wooley, T.D. Near-Optimal Mean Value Estimates for Multidimensional Weyl Sums. Geom. Funct. Anal. 23, 1962–2024 (2013). https://doi.org/10.1007/s00039-013-0242-7

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  • DOI: https://doi.org/10.1007/s00039-013-0242-7

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