Weyl's Inequality, Hua's Inequality, and Waring's Problem

DOI10.1112/jlms/s2-38.2.216zbMath0619.10046OpenAlexW2061688462MaRDI QIDQ3755528

D. R. Heath-Brown

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1112/jlms/s2-38.2.216

zbMATH Keywords

Waring problemsharper boundcubic sumsWeyl's inequalityHua's inequalityHardy-Littlewood asymptotic formulasmall exponent

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Applications of the Hardy-Littlewood method (11P55) Estimates on character sums (11L40)

Related Items (21)

On the Vinogradov mean value ⋮ HUA‐TYPE ITERATION FOR MULTIDIMENSIONAL WEYL SUMS ⋮ Mean value estimates for odd cubic Weyl sums ⋮ A light-weight version of Waring's problem ⋮ Rational points on an intersection of diagonal forms ⋮ On a certain nonary cubic form and related equations ⋮ Multigrade efficient congruencing and Vinogradov's mean value theorem ⋮ On Vinogradov's mean value theorem ⋮ The asymptotic formula in Waring's problem ⋮ On Weyl sums for smaller exponents ⋮ Vinogradov's mean value theorem via efficient congruencing ⋮ Vinogradov's mean value theorem via efficient congruencing. II ⋮ A note on Weyl's inequality for eighth powers ⋮ Small solutions of diagonal congruences ⋮ Some Fourier series with gaps ⋮ The asymptotic formula in Waring's problem for one square and seventeen fifth powers ⋮ DAVENPORT'S METHOD AND SLIM EXCEPTIONAL SETS: THE ASYMPTOTIC FORMULAE IN WARING'S PROBLEM ⋮ On van der Corput's method for exponential sums ⋮ A Diophantine inequality with four squares and one $k$th power of primes ⋮ Small fractional parts of additive forms ⋮ The value of additive forms at prime arguments

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