On the Waring–Goldbach problem for seventh and higher powers

Angel  Kumchev; Trevor D Wooley

doi:10.1007/s00605-016-0936-7

On the Waring–Goldbach problem for seventh and higher powers

Angel Kumchev, Trevor D Wooley

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

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Abstract

We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function H(k) in the Waring-Goldbach problem. We obtain new results for all exponents k≥7, and in particular establish that for large k one has H(k)≤(4k−2)logk−(2log2−1)k−3.

Original language	English
Pages (from-to)	303–310
Number of pages	8
Journal	Monatshefte für Mathematik
Volume	183
Issue number	2
Early online date	15 Jun 2016
DOIs	https://doi.org/10.1007/s00605-016-0936-7
Publication status	Published - 5 May 2017

Keywords

Vinogradov mean-value theorem
Waring–Goldbach problem
Weyl sums

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10.1007/s00605-016-0936-7

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http://arxiv.org/abs/1602.08592

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title = "On the Waring–Goldbach problem for seventh and higher powers",

abstract = "We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function H(k) in the Waring-Goldbach problem. We obtain new results for all exponents k≥7, and in particular establish that for large k one has H(k)≤(4k−2)logk−(2log2−1)k−3.",

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AU - Wooley, Trevor D

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AB - We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function H(k) in the Waring-Goldbach problem. We obtain new results for all exponents k≥7, and in particular establish that for large k one has H(k)≤(4k−2)logk−(2log2−1)k−3.

KW - Vinogradov mean-value theorem

KW - Waring–Goldbach problem

KW - Weyl sums

UR - https://www.scopus.com/pages/publications/84974808835

U2 - 10.1007/s00605-016-0936-7

DO - 10.1007/s00605-016-0936-7

M3 - Article (Academic Journal)

AN - SCOPUS:84974808835

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IS - 2

ER -

On the Waring–Goldbach problem for seventh and higher powers

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