Near-optimal mean value estimates for multidimensional Weyl sums

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.

References in corpus (2)

• Vinogradov's mean value theorem via efficient congruencing, II
• Solution-free sets for sums of binary forms

Cited by in corpus (1)

• Decoupling for two quadratic forms in three variables: a complete characterization