Effective Vinogradov's mean value theorem via efficient boxing

Raphael S. Steiner

doi:10.1016/j.jnt.2019.04.010

Effective Vinogradov's mean value theorem via efficient boxing

Raphael S. Steiner

School of Mathematics

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

1 Citation (Scopus)

Abstract

We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.

Original language	English
Pages (from-to)	354-404
Number of pages	51
Journal	Journal of Number Theory
Volume	204
Early online date	17 May 2019
DOIs	https://doi.org/10.1016/j.jnt.2019.04.010
Publication status	Published - 1 Nov 2019

Keywords

Effective Vinogradov's mean value theorem
Exponential sums
Hardy–Littlewood method

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10.1016/j.jnt.2019.04.010

https://arxiv.org/abs/1603.02536

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title = "Effective Vinogradov's mean value theorem via efficient boxing",

abstract = "We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.",

keywords = "Effective Vinogradov's mean value theorem, Exponential sums, Hardy–Littlewood method",

author = "Steiner, {Raphael S.}",

year = "2019",

month = nov,

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doi = "10.1016/j.jnt.2019.04.010",

language = "English",

volume = "204",

pages = "354--404",

journal = "Journal of Number Theory",

issn = "0022-314X",

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PY - 2019/11/1

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N2 - We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.

AB - We combine Wooley's efficient congruencing method with earlier work of Vinogradov and Hua to get effective bounds on Vinogradov's mean value theorem.

KW - Effective Vinogradov's mean value theorem

KW - Exponential sums

KW - Hardy–Littlewood method

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U2 - 10.1016/j.jnt.2019.04.010

DO - 10.1016/j.jnt.2019.04.010

M3 - Article (Academic Journal)

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VL - 204

SP - 354

EP - 404

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -

Effective Vinogradov's mean value theorem via efficient boxing

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Keywords

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