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The Hardy-Littlewood property of flag varieties

Published online by Cambridge University Press:  22 January 2016

Takao Watanabe
Takao Watanabe*
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka, 560-0043, Japan, [email protected]
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Abstract

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We study the asymptotic distribution of rational points on a generalized flag variety which are of bounded height and satisfy some congruence conditions in the formulation analogous to a strongly Hardy-Littlewood variety.

Keywords

14G0511G35
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 170 , 2003 , pp. 185 - 211
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2003

References

[B] Borel, A., Linear Algebraic Groups, Springer Verlag, 1991.Google Scholar
[BW] Borel, A. and Wallach, N., Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups, Princeton Univ. Press, 1980.Google Scholar
[BR] Borovoi, M. and Rudnick, Z., Hardy-Littlewood varieties and semisimple groups, Invent. Math., 119 (1995), 37–66.CrossRefGoogle Scholar
[DRS] Duke, W., Rudnick, Z. and Sarnak, P., Density of integer points on affine homogeneous varieties, Duke Math. J., 71 (1993), 143–179.CrossRefGoogle Scholar
[FMT] Franke, J., Manin, Y. I. and Tschinkel, Y., Rational points of bounded height on Fano varieties, Invent. Math., 95 (1989), 421–435.Google Scholar
[G] Godement, R., Domaines fondamentaux des groupes arithmétiques, Exp. 257, Sém. Bourbaki, 15 (1962/1963).Google Scholar
[H] Harish-Chandra, , Automorphic Forms on Semisimple Lie Groups, Lec. Notes in Math. 62, Springer Verlag, 1986.Google Scholar
[I] Ikeda, T., On the residue of the Eisenstein series and the Siegel-Weil formula, Comp. Mathematics., 103 (1996), 183–218.Google Scholar
[Lai] Lai, K. F., Tamagawa number of reductive algebraic groups, Comp. Math., 47 (1980), 153–188.Google Scholar
[L] Langlands, R. P., The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups, Proc. Symp. Pure Math. 9, Amer. Math. Soc. (1966), 143–148.Google Scholar
[MW] Moeglin, C. and Waldspurger, J.-L., Spectral Decomposition and Eisenstein Series, Cambridge Univ. Press, 1995.Google Scholar
[MW1] Morishita, M. and Watanabe, T., On S-Hardy-Littlewood homogeneous spaces, Int. J. Math., 9 (1998), 723–757.Google Scholar
[MW2] Morishita, M. and Watanabe, T., Adele geometry of numbers, Class Field Theory - Its Centenary and Prospect, Adv. Studies in Pure Math. 30, Japan Math. Soc. (2001), pp. 509–536.Google Scholar
[S] Sato, A., Counting rational points on projective space with certain congruent conditions, preprint.Google Scholar
[W] Watanabe, T., On an analog of Hermite’s constant, J. Lie Theory, 10 (2000), 33–52.Google Scholar