On the Hasse principle for quartic hypersurfaces

DOI10.1215/00127094-2019-0025zbMath1457.11138arXiv1712.07594OpenAlexW3102451782MaRDI QIDQ2336102

Pankaj Vishe, Oscar Marmon

Publication date: 18 November 2019

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.07594

zbMATH Keywords

rational pointscircle methodquartic formHasse principleVan der Corput differencing

Mathematics Subject Classification ID

Applications of the Hardy-Littlewood method (11P55) Rational points (14G05) Counting solutions of Diophantine equations (11D45) Cubic and quartic Diophantine equations (11D25)

Related Items (2)

A quantitative Hasse principle for weighted quartic forms ⋮ On the Hasse principle for complete intersections

Cites Work

• Cubic hypersurfaces and a version of the circle method for number fields
• On the number of points on a complete intersection over a finite field. (Appendix: Number of points on singular complete intersections by Nicholas M. Katz)
• A new iterative method in Waring's problem
• Bounds for automorphic \(L\)-functions
• Rational curves on smooth hypersurfaces of low degree
• Improvements in Birch's theorem on forms in many variables
• Cubic forms in 14 variables
• On octonary cubic forms
• Pairs of quadrics in 11 variables
• Forms in many variables
• Rational points on quartic hypersurfaces
• A new form of the circle method, and its application to quadratic forms.
• Cubic Forms in Ten Variables
• Arithmetic of diagonal quartic surfaces, II
• The density of integral points on hypersurfaces of degree at least four
• THE DENSITY OF INTEGRAL POINTS ON COMPLETE INTERSECTIONS
• On a Principle of Lipschitz
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