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arXiv · 1205.6331

Near-optimal mean value estimates for multidimensional Weyl sums

Scott T. Parsell·Sean M. Prendiville·Trevor D. Wooley
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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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Scott T. Parsell, Sean M. Prendiville, Trevor D. Wooley. 2012-05-29. Near-optimal mean value estimates for multidimensional Weyl sums. https://arxiv.org/abs/1205.6331

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