Optimal mean value estimates beyond Vinogradov's mean value theorem

DOI10.4064/AA200824-9-3zbMath1497.11191arXiv1901.03153OpenAlexW3205337625MaRDI QIDQ5030086

Julia Brandes, Trevor D. Wooley

Publication date: 15 February 2022

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

Full work available at URL: https://arxiv.org/abs/1901.03153

zbMATH Keywords

exponential sumsHardy-Littlewood method

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Applications of the Hardy-Littlewood method (11P55) Counting solutions of Diophantine equations (11D45) Weyl sums (11L15)

Cites Work

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• The Hasse principle for systems of diagonal cubic forms
• The cubic case of the main conjecture in Vinogradov's mean value theorem
• Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three
• Rational solutions of certain equations involving norms
• The Hasse principle for pairs of diagonal cubic forms
• Simultaneous Additive Equations: Repeated and Differing Degrees
• The Hasse Principle for Systems of Quadratic and Cubic Diagonal Equations
• VINOGRADOV SYSTEMS WITH A SLICE OFF
• Rational solutions of pairs of diagonal equations, one cubic and one quadratic
• Simultaneous Quadratic Equations
• Simultaneous quadratic equations II
• Nested efficient congruencing and relatives of Vinogradov's mean value theorem

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