Sums and differences of three \(k\)th powers

DOI10.1016/j.jnt.2009.01.012zbMath1182.11017arXiv0806.4330OpenAlexW2064864727MaRDI QIDQ1019859

D. R. Heath-Brown

Publication date: 28 May 2009

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4330

zbMATH Keywords

rational pointsternary formspower free values of polynomialssums of three powers

Mathematics Subject Classification ID

Counting solutions of Diophantine equations (11D45) Varieties over global fields (11G35) Higher degree equations; Fermat's equation (11D41) Distribution of primes (11N05) Primes represented by polynomials; other multiplicative structures of polynomial values (11N32) Representation problems (11D85)

Related Items (4)

Rational points close to non‐singular algebraic curves ⋮ Sums and differences of four \(k\)th powers ⋮ The density of twins of k -free numbers ⋮ Power‐free values of polynomials

Cites Work

• Power-free values, large deviations, and integer points on irrational curves
• The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène).
• On Thue's equation
• The number of integral points on arcs and ovals
• Counting rational points on hypersurfaces of low dimension
• Counting Rational Points on Algebraic Varieties
• Power-free values, repulsion between points, differing beliefs and the existence of error
• Power Free Values of Polynomials II
• The rational points close to a curve II
• The rational points close to a curve III
• On the power free values of polynomials
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