Rational Points of Bounded Height on Compactifications of Anisotropic Tori

1994/11/15 by Victor V. Batyrev, Yuri Tschinkel, Batyrev, Victor V. +1 · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.alg-geom/9411009

openalex publication_date 1994/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Rational points of bounded height on Fano varieties

Cited by

• M-points of bounded height on toric varieties
• Equivariant unirationality of tori in small dimensions

Related

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• Distribution of rational points of bounded height on equivariant compactifications of PGL₂ I
• Height Zeta Functions of Toric Varieties
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• Height zeta functions of equivariant compactifications of unipotent groups