The cubic case of the main conjecture in Vinogradov's mean value theorem

By Trevor D. Wooley. 2014

168 citations recorded by the source corpus.

Abstract We apply a variant of the multigrade efficient congruencing method to estimate Vinogradov's integral of degree 3 for moments of order 2 s , 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.

Subfields: Algebra and Number Theory, Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/5ed5e8c81df2467a92f2bbac1c04b406f8d67020

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In Algebra and Number Theory

1. Larry Guth
2. Jean Bourgain
3. Trevor D. Wooley
4. Ciprian Demeter
5. P. P. Varj'u
6. Ilya D. Shkredov
7. Peter Sarnak
8. Harald Andrés Helfgott

In Applied Mathematics

1. Ciprian Demeter
2. Larry Guth
3. Jean Bourgain
4. Xiumin Du
5. Ruixiang Zhang
6. Jonathan Bennett
7. J. Hickman
8. Keith McKenzie Rogers

Citations in the corpus

• Nested efficient congruencing and relatives of Vinogradov's mean value theorem (2017, methodology): “The analysis of [55, 57, 60] iterates the relation (2.”
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three (2015, methodology): “The case n = 3 was solved by Wooley in [21], a major achievement of his remarkable efficient congruencing method.”