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.
Original language | English |
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Pages (from-to) | 1962-2024 |
Number of pages | 63 |
Journal | Geometric and Functional Analysis |
Volume | 23 |
Issue number | 6 |
Early online date | 6 Jul 2013 |
DOIs | |
Publication status | Published - Dec 2013 |
Keywords
- VALUE THEOREM
- POINTS