On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing

DOI10.1007/s11511-014-0119-0zbMath1307.11102arXiv1304.6917OpenAlexW2133848721MaRDI QIDQ483370

Kevin Ford, Trevor D. Wooley

Publication date: 17 December 2014

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.6917

zbMATH Keywords

circle methodWaring's problemefficient congruencingVinogradov's mean value theorem

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Applications of the Hardy-Littlewood method (11P55) Weyl sums (11L15)

Related Items (10)

The cubic case of the main conjecture in Vinogradov's mean value theorem ⋮ On the Vinogradov mean value ⋮ Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three ⋮ Multigrade efficient congruencing and Vinogradov's mean value theorem ⋮ The cubic case of Vinogradov's mean value theorem ⋮ On higher dimensional Poissonian pair correlation ⋮ APPROXIMATING THE MAIN CONJECTURE IN VINOGRADOV'S MEAN VALUE THEOREM ⋮ Rational lines on cubic hypersurfaces ⋮ The asymptotic estimates and Hasse principle for multidimensional Waring's problem ⋮ On integer solutions of Parsell-Vinogradov systems

Cites Work

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• Vinogradov's mean value theorem via efficient congruencing
• A note on simultaneous congruences
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• The Asymptotic Formula in Waring’s Problem
• A NEW ESTIMATE OF AN INTEGRAL OF I. M. VINOGRADOV
• Quasi-Diagonal Behaviour in Certain Mean Value Theorems of Additive Number Theory
• A special case of Vinogradov's mean value theorem
• Weyl's inequality and exponential sums over binary forms

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