References
V. Batyrev and Yu. I. Manin, “Sur le nombre des points rationnels de hauteur bornée des variétés algébriques,”Math. Ann.,286, 27–43 (1990).
V. Batyrev and Yu. Tschinkel, “Rational points of bounded height on compactifications of anisotropic tori,”Int. Math. Res. Notices,12, 591–635 (1995).
V. Batyrev and Yu. Tschinkel,Manin's conjecture for toric varieties, Preprint IHES (1995).
J. L. Brylinski, “Décomposition simpliciale d'un réseau, invariante par un group fini d'automorphismes,”C. R. Acad. Sci. Paris, Sér. A-B,288, A137-A139 (1979).
V. I. Danilov, “The geometry of toric varieties,”Russ. Math. Surveys,33, No. 2, 97–154 (1978).
P. K. J. Draxl, “L-Funktionen algebraischer Tori,”J. Number Theory,3, No. 4, 444–467 (1971).
M. Köcher, “Positivitätsbereiche im Rn,”Amer. J. Math.,79, 575–596 (1957).
T. Ono, “Arithmetic of algebraic tori,”Ann. Math.,74, 101–139 (1961).
T. Ono, “On the Tamagawa number of algebraic tori,”Ann. Math.,78, 47–73 (1963).
E. Peyre, “Hauteurs et nombres de Tamagawa sur les variétés de Fano,”Duke Math. J.,79, 101–218 (1995).
O. S. Rothaus, “Domains of positivity,”Abh. Math. Sem. Univ. Hamburg,24, 189–235 (1960).
H. Rademacher, “On the Phragmén-Lindelöf principle and some applications,”Math. Z.,72, 192–204 (1959).
E. B. Vinberg, “The theory of convex homogeneous cones,”Tr. Mosk. Mat. Obshch.,12, 340–403 (1963).
V. E. Voskresenskii, “Projective invariant Demazure models,”Math. USSR Izv.,20, 189–202 (1983).
Additional information
Translaed from Itogi Naukii Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 34. Algebraic Geometry-5, 1996.
Rights and permissions
About this article
Cite this article
Batyrev, V., Tschinkel, Y. Height zeta functions of toric varieties. J Math Sci 82, 3220–3239 (1996). https://doi.org/10.1007/BF02362469
Issue Date:
DOI: https://doi.org/10.1007/BF02362469