Height of rational points on random Fano hypersurfaces
Pierre Le Boudec
TL;DR
This paper studies the minimal height of rational points on Fano hypersurfaces over rationals, establishing an average version of Manin's conjecture for these varieties, revealing statistical patterns in rational point distribution.
Contribution
It introduces a statistical analysis of rational point heights on Fano hypersurfaces and proves an average case of Manin's conjecture for this family.
Findings
Average height of rational points analyzed
Proved an average version of Manin's conjecture
Identified statistical distribution patterns
Abstract
We investigate in a statistical fashion the smallest height of a rational point on a Fano hypersurface defined over the field of rational numbers. Along the way, we establish an average version of Manin's conjecture about the number of rational points of bounded height on Fano varieties for the complete family of Fano hypersurfaces of fixed degree and dimension.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Meromorphic and Entire Functions