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

8 Citations (Scopus)

291 Downloads (Pure)

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

Access to Document

10.1112/S0025579316000279

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://doi.org/10.1112/S0025579316000279. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 550 KB

Handle.net

Persistent link

Cite this

@article{fbb8bb8ed48c4eb391382c3f96e7132c,

title = "Approximating the main conjecture in Vinogradov's mean value theorem",

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) ",

keywords = "math.NT, 11L15, 11L07, 11P55",

author = "Wooley, {Trevor D.}",

year = "2017",

month = jan,

day = "2",

doi = "10.1112/S0025579316000279",

language = "English",

volume = "63",

pages = "292--350",

journal = "Mathematika",

issn = "0025-5793",

publisher = "University College London",

number = "1",

}

TY - JOUR

T1 - Approximating the main conjecture in Vinogradov's mean value theorem

AU - Wooley, Trevor D.

PY - 2017/1/2

Y1 - 2017/1/2

N2 - 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)

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)

KW - math.NT

KW - 11L15

KW - 11L07

KW - 11P55

U2 - 10.1112/S0025579316000279

DO - 10.1112/S0025579316000279

M3 - Article (Academic Journal)

SN - 0025-5793

VL - 63

SP - 292

EP - 350

JO - Mathematika

JF - Mathematika

IS - 1

ER -

Approximating the main conjecture in Vinogradov's mean value theorem

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Cite this