Near-optimal mean value estimates for multidimensional Weyl sums

DOI10.1007/s00039-013-0242-7zbMath1320.11028arXiv1205.6331OpenAlexW2094211546MaRDI QIDQ2636915

Scott T. Parsell, Sean Prendiville, Trevor D. Wooley

Publication date: 18 February 2014

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.6331

zbMATH Keywords

exponential sumsHardy-Littlewood methodDiophantine equationsVinogradov's mean value theorem

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) Weyl sums (11L15)

Related Items (18)

On the Vinogradov mean value ⋮ Strichartz estimates for the Schroedinger equation on non-rectangular two-dimensional tori ⋮ Sharp bounds for the cubic Parsell-Vinogradov system in two dimensions ⋮ Decoupling for two quadratic forms in three variables: a complete characterization ⋮ Mean value estimates for Weyl sums in two dimensions ⋮ Discrete restriction estimates for forms in many variables ⋮ A note on the real densities of homogeneous systems in function fields ⋮ Rational lines on cubic hypersurfaces ⋮ A Bombieri-Vinogradov theorem with products of Gaussian primes as moduli ⋮ Forms in many variables and differing degrees ⋮ Decoupling for moment manifolds associated to Arkhipov-Chubarikov-Karatsuba systems ⋮ Burgess bounds for multi-dimensional short mixed character sums ⋮ On Properties of Polynomials in Random Elements ⋮ The asymptotic estimates and Hasse principle for multidimensional Waring's problem ⋮ On integer solutions of Parsell-Vinogradov systems ⋮ Vinogradov’s Mean Value Theorem as an Ingredient in Polynomial Large Sieve Inequalities and Some Consequences ⋮ Uniform bounds in Waring's problem over some diagonal forms ⋮ Large sieve estimate for multivariate polynomial moduli and applications

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