69 citations · 615 across the 125 of their papers we have counts for
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Tamagawa numbers of polarized algebraic varieties
Victor V. Batyrev, Yu. Tschinkel
Let be an ample metrized invertible sheaf on a smooth quasi-projective algebraic variety defined over a number field. Denote by $N(V,{\cal L},B)…
Height zeta functions of toric bundles over flag varieties
Matthias Strauch, Yuri Tschinkel
We investigate analytic properties of height zeta functions of toric bundles over flag varieties.
Rational points on some Fano cubic bundles
Victor V. Batyrev, Yuri Tschinkel
We consider some families of smooth Fano hypersurfaces in given by a homogeneous polynomial of bidegree . For these varieties we o…
Manin's conjecture for toric varieties
Victor V. Batyrev, Yuri Tschinkel
We prove an asymptotic formula conjectured by Manin for the number of -rational points of bounded height with respect to the anticanonical line bundle for arbitrary smooth proje…
Rational Points of Bounded Height on Compactifications of Anisotropic Tori
Victor V. Batyrev, Yuri Tschinkel
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 c…