Integral points on quadratic twists and linear growth for certain elliptic fibrations

2013/07/31 by Pierre Le Boudec, Boudec, Pierre Le
Mathematics · #11D45 #11G05 #14G05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11D45 #msc:11G05 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1308.0060

arxiv created 2013/07/31 · arxiv updated 2013/08/02

Abstract

We prove that the number of rational points of bounded height on certain del Pezzo surfaces of degree 1 defined over Q grows linearly, as predicted by Manin's conjecture. Along the way, we investigate the average number of integral points of small naive height on quadratic twists of a fixed elliptic curve with full rational 2-torsion.

Related

• Number of integral points on quadratic twists of elliptic curves
• Almost all quadratic twists of an elliptic curve have no integral points
• Integral Points on a del Pezzo Surface over Imaginary Quadratic Fields
• Counting points on a family of degree one del Pezzo surfaces
• Counting integral points on universal torsors