Approximating the main conjecture in Vinogradov's mean value theorem

Trevor D. Wooley

doi:10.1112/S0025579316000279

Approximating the main conjecture in Vinogradov's mean value theorem

Trevor D. Wooley

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1≤s≤12k(k+1)−13k+o(k). In particular, as k→∞, we confirm the main conjecture in Vinogradov's mean value theorem for 100% of the critical interval 1≤s≤12k(k+1)

Original language	English
Pages (from-to)	292-350
Number of pages	59
Journal	Mathematika
Volume	63
Issue number	1
DOIs	https://doi.org/10.1112/S0025579316000279
Publication status	Published - 2 Jan 2017

Keywords

math.NT
11L15
11L07
11P55

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abstract = "We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1≤s≤12k(k+1)−13k+o(k). In particular, as k→∞, we confirm the main conjecture in Vinogradov's mean value theorem for 100\% of the critical interval 1≤s≤12k(k+1) ",

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AB - We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1≤s≤12k(k+1)−13k+o(k). In particular, as k→∞, we confirm the main conjecture in Vinogradov's mean value theorem for 100% of the critical interval 1≤s≤12k(k+1)

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KW - 11L15

KW - 11L07

KW - 11P55

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DO - 10.1112/S0025579316000279

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JO - Mathematika

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IS - 1

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Approximating the main conjecture in Vinogradov's mean value theorem

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