Abstract
We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov's integral of degree 3 for moments of order 2s, establishing strongly diagonal behaviour for 1 ≤ s ≤ 6. Consequently, the main conjecture is now known to hold for the first time in a case of degree exceeding 2.
Original language | English |
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Pages (from-to) | 532-561 |
Number of pages | 30 |
Journal | Advances in Mathematics |
Volume | 294 |
Early online date | 21 Mar 2016 |
DOIs | |
Publication status | Published - 14 May 2016 |
Keywords
- math.NT
- 11L15
- 11L07
- 11P55