Abstract
We explain our approach to the problem of counting rational points of bounded height on equivariant compactifications of semi-simple groups.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
V. V. Batyrev & Y. I. Manin — Sur le nombre des points rationnels de hauteur borné des variétés algébriques, Math. Ann. 286 (1990), no. 1-3, 27–43.
V. V. Batyrev & Yu. Tschinkel — Manin’s conjecture for toric varieties, J. Algebraic Geom. 7 (1998), no. 1, 15–53.
V. V. Batyrev & Y. Tschinkel — Tamagawa numbers of polarized algebraic varieties, Nombre et répartition des points de hauteur bornée, Astérisque, no. 251, 1998, 299–340.
A. Chambert-Loir & Y. Tschinkel — On the distribution of points of bounded height on equivariant compactifications of vector groups, Invent. Math. 148 (2002), no. 2, 421–452.
C. De Concini & C. Procesi — Complete symmetric varieties, Invariant theory (Montecatini, 1982), Lecture Notes in Math., vol. 996, Springer, Berlin, 1983, 1–44.
G. B. Folland — Introduction to Partial Differential Equations, Princeton University Press, Princeton, N.J., 1976.
J. Franke, Y. I. Manin & Y. Tschinkel — Rational points of bounded height on Fano varieties, Invent. Math. 95 (1989), no. 2, 421–435.
S. Gelbart & H. Jacquet — Forms of GL(2) from the analytic point of view, Automorphic Forms, Representations and L-functions, Part 1, Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc, Providence, R.I., 1979, 213–251.
S. Gelbart & F. Shahidi — Boundedness of automorphic L-functions in vertical strips, J. Amer. Math. Soc. 14 (2001), no. 1, 79–107 (electronic).
H. H. Kim & F. Shahidi — Functorial products for GLb2 × GLb3 and the symmetric cube for GLb2, Ann. of Math. (2)155 (2002), no. 3, 837–893.
A. W. Knapp — Representation Theory of Semisimple Groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 2001.
W. Müller — The trace class conjecture in the theory of automorphic forms, Ann. of Math. (2)130 (1989), no. 3, 473–529.
W. Müller, On the spectral side of the Arthur trace formula, 2002, preprint.
E. Peyre — Hauteurs et mesures de Tamagawa sur les variétés de Fano, Duke Math. J. 79 (1995), 101–218.
D. Ramakrishnan — Modularity of the Rankin-Selberg L-series, and multiplicity one for SL(2), Ann. of Math. (2)152 (2000), no. 1, 45–111.
J. Shalika, R. Takloo-Bighash & Y. Tschinkel — Rational points on compactifications of anisotropic forms of semi-simple groups, 2003.
J. Shalika & Y. Tschinkel — Height zeta functions of equivariant compactifications of the Heisenberg group, ArXiV:math.NT/0203093, to appear, 2003.
M. Strauch & Y. Tschinkel — Height zeta functions of toric bundles over flag varieties, Selecta Math. (N.S.) 5 (1999), no. 3, 325–396.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Shalika, J., Takloo-Bighash, R., Tschinkel, Y. (2004). Rational Points on Compactifications of Semi-Simple Groups of Rank 1. In: Poonen, B., Tschinkel, Y. (eds) Arithmetic of Higher-Dimensional Algebraic Varieties. Progress in Mathematics, vol 226. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8170-8_13
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8170-8_13
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6471-2
Online ISBN: 978-0-8176-8170-8
eBook Packages: Springer Book Archive