Rational Points of Bounded Height on Compactifications of Anisotropic Tori
Victor V. Batyrev, Yuri Tschinkel
TL;DR
This paper studies the distribution of rational points of bounded height on certain algebraic varieties, using zeta-functions to verify conjectures about their density and distribution over number fields.
Contribution
It introduces a new analytic approach to analyze heights on equivariant compactifications of anisotropic tori, confirming conjectures about rational point distribution.
Findings
Verified conjectures on rational point distribution
Established properties of associated zeta-functions
Provided new insights into heights on algebraic tori
Abstract
We investigate the analytic properties of the zeta-function associated with heights on equivariant compactifications of anisotropic tori over number fields. This allows to verify conjectures about the distribution of rational points of bounded height.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Advanced Combinatorial Mathematics