Further improvements in Waring's problem

DOI10.1007/BF02392467zbMath0849.11075WikidataQ102179198 ScholiaQ102179198MaRDI QIDQ1901115

Trevor D. Wooley, Robert C. Vaughan

Publication date: 12 November 1996

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

zbMATH Keywords

Waring's problemrepresentation of integerssums of higher powershigher differencesupper bounds for \(G(k)\)first differenceHardy-Littlewood dissectionsiterating on minor arcs

Mathematics Subject Classification ID

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

Related Items (25)

Equal sums of three powers ⋮ Breaking classical convexity in Waring's problem: sums of cubes and quasi-diagonal behaviour ⋮ On Waring's problem for larger powers ⋮ A quasi-paucity problem ⋮ Modular hyperbolas ⋮ Analytic number theory. Abstracts from the workshop held November 6--12, 2022 ⋮ On Vu's thin basis theorem in Waring's problem ⋮ Waring's problem for Beatty sequences and a local to global principle ⋮ On Weyl's inequality, Hua's lemma, and exponential sums over binary forms. ⋮ Rational lines on cubic hypersurfaces ⋮ Quasi-Diagonal Behaviour in Certain Mean Value Theorems of Additive Number Theory ⋮ On Waring’s problem: Three cubes and a sixth power ⋮ Concentration of points on two and three dimensional modular hyperbolas and applications ⋮ Further improvements in Waring's problem. II: Sixth powers ⋮ Representation by sums of unlike powers ⋮ Even ascending powers ⋮ CONCENTRATION OF POINTS ON MODULAR QUADRATIC FORMS ⋮ On Waring's problem for intermediate powers ⋮ Waring's problem in function fields ⋮ The representation of almost all numbers as sums of unlike powers ⋮ A Sidon basis ⋮ The density of rational lines on cubic hypersurfaces ⋮ Sums of three cubes, II ⋮ Local and global theory for the three-wave mixing Schrödinger system with quadratic interactions on Zoll manifolds ⋮ Waring's problem with digital restrictions

Cites Work

• Unnamed Item
• Unnamed Item
• A new iterative method in Waring's problem
• Large improvements in Waring's problem
• Equations over finite fields. An elementary approach
• Further improvements in Waring's problem. II: Sixth powers
• On Waring's Problem for Smaller Exponents
• On Waring's Problem for Sixth Powers
• A New Iterative Method in Waring's Problem II
• On Waring's Problem for Fifth Powers and Some Related Topics
• On Waring's Problem: Some Refinements
• Further improvements in Waring’s problem. Ill Eighth powers
• New Estimates for Smooth Weyl Sums
• On exponential sums over smooth numbers.

This page was built for publication: Further improvements in Waring's problem