The density of rational points on non-singular hypersurfaces

DOI10.1007/BF02830871zbMath0808.11042MaRDI QIDQ1322358

D. R. Heath-Brown

Publication date: 9 March 1995

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

zbMATH Keywords

hypersurfacerational pointscounting functionsingular locusnumber of pointsDeligne's bounds for exponential sumshypersurfaces over finite fieldsmultiple exponential sum

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Rational points (14G05) Arithmetic algebraic geometry (Diophantine geometry) (11G99)

Related Items

On the density of integer points on generalised Markoff-Hurwitz and Dwork hypersurfaces, On a question of Heath-Brown: Good estimates on average for higher degree Kloosterman sums, Counting rational points on projective varieties, Nonlinear laminates where the effective conductivity is integer valued, Counting rational points on smooth cyclic covers, Counting Rational Points on Cubic Hypersurfaces, On the density of rational and integral points on algebraic varieties, Rational points on quartic hypersurfaces, On the saturation number for cubic surfaces

Cites Work

• 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)
• Rational points of bounded height on Fano varieties
• Forms in many variables
• The Distribution of Galois Groups and Hilbert's Irreducibility Theorem
• Cubic Forms in Ten Variables
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