Near-optimal Mean Value Estimates for Multidimensional Weyl Sums

  title={Near-optimal Mean Value Estimates for Multidimensional Weyl Sums},
  author={Scott T. Parsell and S. M. PRENDIVILLE and Trevor D. Wooley},
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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