Counting rational points on smooth cyclic covers

DOI10.1016/j.jnt.2012.02.010zbMath1248.14027arXiv1109.1455OpenAlexW2011977048MaRDI QIDQ423619

D. R. Heath-Brown, Lillian Beatrix Pierce

Publication date: 4 June 2012

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

Full work available at URL: https://arxiv.org/abs/1109.1455

zbMATH Keywords

rational pointscharacter sumscyclic coverspower sieve

Mathematics Subject Classification ID

Rational points (14G05) Counting solutions of Diophantine equations (11D45) Estimates on character sums (11L40)

Related Items

On the density of integer points on generalised Markoff-Hurwitz and Dwork hypersurfaces, A Diophantine problem about Kummer surfaces, Geometric generalizations of the square sieve, with an application to cyclic covers, Uniform bounds for rational points on hyperelliptic fibrations, Burgess bounds for short character sums evaluated at forms, Arithmetic exponent pairs for algebraic trace functions and applications

Cites Work

• Unnamed Item
• Unnamed Item
• Density of rational points on cyclic covers of \(\mathbb{P}^n\)
• The square sieve and consecutive square-free numbers
• The density of rational points on non-singular hypersurfaces
• Rational points on finite covers of \({\mathbb P}^{1}\) and \({\mathbb P}^{2}\)
• The density of rational points on curves and surfaces. (With an appendix by J.-L. Colliot-Thélène).
• La conjecture de Weil. I
• A bound for the 3-part of class numbers of quadratic fields by means of the square sieve
• Imaginary quadratic fields with class group exponent 5
• Rational points on quartic hypersurfaces
• A new form of the circle method, and its application to quadratic forms.
• Estimates for Nonsingular Mixed Character Sums