On the Waring-Goldbach problem for seventh and higher powers

DOI10.1007/s00605-016-0936-7zbMath1381.11099arXiv1602.08592OpenAlexW1876671860MaRDI QIDQ2360560

Angel V. Kumchev, Trevor D. Wooley

Publication date: 4 July 2017

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.08592

zbMATH Keywords

Waring-Goldbach problemWeyl sumsVinogradov mean-value theorem

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Goldbach-type theorems; other additive questions involving primes (11P32) Applications of the Hardy-Littlewood method (11P55) Sums over primes (11L20)

Related Items (12)

Rational lines on cubic hypersurfaces ⋮ A hybrid of two theorems of Piatetski-Shapiro ⋮ On Waring-Goldbach problem with Piatetski-Shapiro primes ⋮ Another Waring–Goldbach problem ⋮ Discrete multilinear maximal functions and number theory ⋮ PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES ⋮ Exceptional sets in Waring-Goldbach problem for fifth powers ⋮ Small prime solutions to diagonal Diophantine equations ⋮ Waring–Goldbach Problem with Piatetski-Shapiro Primes ⋮ On exceptional sets of biquadratic Waring-Goldbach problem ⋮ On the ergodic Waring-Goldbach problem ⋮ Uniform bounds in Waring's problem over some diagonal forms

Cites Work

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• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Vinogradov's mean value theorem via efficient congruencing
• On the Waring-Goldbach Problem for Fourth and Fifth Powers
• Multigrade efficient congruencing and Vinogradov's mean value theorem
• On the Waring–Goldbach problem for eighth and higher powers
• On the Waring–Goldbach problem for seventh powers
• On the Waring-Goldbach problem for fourth and sixth powers
• SOME RESULTS IN THE ADDITIVE PRIME-NUMBER THEORY

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