Rational solutions of pairs of diagonal equations, one cubic and one quadratic

DOI10.1112/plms/pdu054zbMath1333.11034arXiv1404.7161OpenAlexW3101267269MaRDI QIDQ5175029

Trevor D. Wooley

Publication date: 19 February 2015

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

Full work available at URL: https://arxiv.org/abs/1404.7161

zbMATH Keywords

diagonal equationsexponential summean valueHasse principleHardy-Littlewood circle methodquadraticcubicsimultaneouspair

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Quadratic and bilinear Diophantine equations (11D09) Diophantine equations in many variables (11D72) Cubic and quartic Diophantine equations (11D25) Weyl sums (11L15)

Related Items (12)

The cubic case of the main conjecture in Vinogradov's mean value theorem ⋮ ON THE INHOMOGENEOUS VINOGRADOV SYSTEM ⋮ Mean value estimates for odd cubic Weyl sums ⋮ On Waring's problem for larger powers ⋮ On Waring's problem: Beyond Freĭman's theorem ⋮ Subconvexity in the inhomogeneous cubic Vinogradov system ⋮ VINOGRADOV SYSTEMS WITH A SLICE OFF ⋮ Small cap decouplings. With an appendix by D. R. Heath-Brown. ⋮ On sums of powers of almost equal primes ⋮ The Hasse principle for diagonal forms restricted to lower-degree hypersurfaces ⋮ Simultaneous cubic and quadratic diagonal equations in 12 prime variables ⋮ Optimal mean value estimates beyond Vinogradov's mean value theorem

Cites Work

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• A New Application of the Hardy-Littlewood-Kloosterman Method
• A problem in additive number theory
• A new form of the circle method, and its application to quadratic forms.
• On simultaneous additive equations, IV
• Sums of three cubes
• Simultaneous Quadratic Equations

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