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

Trevor D Wooley

doi:10.1016/j.aim.2016.02.033

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

Trevor D Wooley

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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
Pages (from-to)	532-561
Number of pages	30
Journal	Advances in Mathematics
Volume	294
Early online date	21 Mar 2016
DOIs	https://doi.org/10.1016/j.aim.2016.02.033
Publication status	Published - 14 May 2016

Keywords

math.NT
11L15
11L07
11P55

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10.1016/j.aim.2016.02.033

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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.",

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AB - 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.

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KW - 11L15

KW - 11L07

KW - 11P55

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DO - 10.1016/j.aim.2016.02.033

M3 - Article (Academic Journal)

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VL - 294

SP - 532

EP - 561

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

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

Abstract

Keywords

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