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A generalization of Vinogradov's mean value theorem

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Publication:5316044
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DOI10.1112/S002461150501525XzbMath1119.11024MaRDI QIDQ5316044

Scott T. Parsell

Publication date: 12 September 2005

Published in: Proceedings of the London Mathematical Society (Search for Journal in Brave)


zbMATH Keywords

multiple exponential sumsmany variablesVinogradov's mean value theoremefficient differencing


Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Applications of the Hardy-Littlewood method (11P55) Counting solutions of Diophantine equations (11D45) Diophantine equations in many variables (11D72)


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HUA‐TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS ⋮ Near-optimal mean value estimates for multidimensional Weyl sums ⋮ Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions ⋮ Vinogradov's mean value theorem via efficient congruencing ⋮ A note on multiple exponential sums in function fields ⋮ Rational lines on cubic hypersurfaces ⋮ Decoupling for moment manifolds associated to Arkhipov-Chubarikov-Karatsuba systems ⋮ Asymptotic estimates for rational linear spaces on hypersurfaces ⋮ The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces ⋮ On integer solutions of Parsell-Vinogradov systems



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