Journal of Mathematical Sciences

, Volume 73, Issue 1, pp 47–113

Adele groups and Siegel-Tamagawa formulas

  • V. E. Voskresenskii
Article
  • 160 Downloads

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    Z. I. Borevich and I. R. Shafarevich,Number Theory [in Russian], Nauka, Moscow (1985).Google Scholar
  2. 2.
    B. A. Venkov, “On an integral invariant of the group of unimodular linear substitutions” [in Russian] In:B.A. Venkov Studies in Number Theory, Selected Works, Nauka, Leningrad (1981), pp. 287–306.Google Scholar
  3. 3.
    V. E. Voskresenskii, “Picard groups of linear algebraic groups” [in Russian] In:Studies in Number Theory, Vol. 3, Saratov University Press, Saratov (1969), pp. 7–16.Google Scholar
  4. 4.
    V. E. Voskresenskii,Algebraic Tori [in Russian], Nauka, Moscow (1977).Google Scholar
  5. 5.
    V. E. Voskresenskii, “Integral structures in algebraic tori,” [in Russian], In:Seminar on Arithmetic of Algebraic Varieties, Saratov University Press, Saratov (1979), pp. 8–15.Google Scholar
  6. 6.
    V. E. Voskresenski, “Projective group of a finite separable extension” [in Russian], In:Arithmetic and Geometry of Manifolds [in Russian], Kuibyshev University Press, Kuibyshev (1988), pp. 27–43.Google Scholar
  7. 7.
    S. G. Gindikin and F. I. Karpelevich, “On an integral related to Riemannian symmetric spaces of positive curvature,”Izv. Akad. Nauk SSSR, Ser. Mat.,30, No. 5, 1147–1154 (1966).MathSciNetGoogle Scholar
  8. 8.
    D. P. Zelobenko,Harmonic Analysis on Semisimple Complex Lie Groups [in Russian], Nauka, Moscow (1974).Google Scholar
  9. 9.
    V. P. Platonov, “Problem of strong approximation and Kneser-Tits conjecture for algebraic groups,”Izv. Akad. Nauk SSSR, Ser. Mat.,33, No. 6, 1211–1219 (1969); with the supplement,Izv. Akad. Nauk SSSR, Ser. Mat.,34, No. 4, 775–777 (1970).MATHMathSciNetGoogle Scholar
  10. 10.
    T. A. Springer, “Linear algebraic groups” [in Russian], In:Advances of Science and Technology. Modern Problems of Math. Main Trends, VINITI (1989).Google Scholar
  11. 11.
    J. W. S. Cassels and A. Frohlich, eds.,Algebraic Number Theory, Academic Press, London-New York (1967).Google Scholar
  12. 12.
    A. Borel, “Some properties of adele groups attached to algebraic groups,”Bull. Amer. Math. Soc.,67, 583–585 (1961).MATHMathSciNetGoogle Scholar
  13. 13.
    A. Borel, “Properties and linear representations of Chevalley groups,”Lect. Notes Math.,131, 1–55 (1970).MathSciNetGoogle Scholar
  14. 14.
    N. Bourbaki,Algèbre, Chap. 4-6., Hermann, Paris (1958).Google Scholar
  15. 15.
    N. Bourbaki,Groupes et Algèbres de Lie, Chap. 1-3, Hermann, Paris (1971–1972).Google Scholar
  16. 16.
    N. Bourbaki,Groupes et Algèbres de Lie, Chap. 4-6, Hermann, Paris (1968).Google Scholar
  17. 17.
    N. Bourbaki,Groupes et Algèbres de Lie, Chap. 7-8, Hermann, Paris (1975).Google Scholar
  18. 18.
    J. W. S. Cassels,Rational Quadratic Forms, Academic Press, London-New York (1978).Google Scholar
  19. 19.
    J. H. Conway and N. J. A. Sloane, “The unimodular lattices of dimension up to 23 and the Minkowski-Siegel mass constants,”Europ. J. Combinatorics,3, 219–231 (1982).MathSciNetGoogle Scholar
  20. 20.
    J. Dieudonné,La Geometrie des Groupes Classiques, Springer, Berlin-Heidelberg-New York (1971).Google Scholar
  21. 21.
    Harish-Chandra,Automorphic Forms on Semisimple Lie Groups, Springer, Berlin-Heidelberg-New York (1968).Google Scholar
  22. 22.
    H. Hasse,Über die Klassenzahl Abelscher Zahlkörper, Akademie Verlag, Berlin (1952).Google Scholar
  23. 23.
    S. Helgason,Differential Geometry and Symmetric Spaces, Academic Press, New York-London (1962).Google Scholar
  24. 24.
    S. Helgason,Groups and Geometric Analysis, Academic Press, New York (1984).Google Scholar
  25. 25.
    S. Katayama, “E(K/k) and other arithmetical invariants for finite Galois extensions,” Nagoya Math. J.,114, 135–142 (1989).MATHMathSciNetGoogle Scholar
  26. 26.
    R. Kottwitz, “Tamagawa numbers,” Ann. Math.,127, 629–646 (1988).MATHMathSciNetGoogle Scholar
  27. 27.
    K. F. Lai, “Tamagawa numbers of reductive algebraic groups,”Compos. Math., 153–188 (1988).Google Scholar
  28. 28.
    S. Lang,Algebraic Numbers, Addison-Wesley (1964).Google Scholar
  29. 29.
    S. Lang,Algebra, Addison-Wesley (1965).Google Scholar
  30. 30.
    R. P. Langlands, “The volume of the fundamental domain for some arithmetical subgroups of Chevalley groups,” In:Algebraic Groups and Discontinuous Subgroups, Providence (1966), pp. 143–148.Google Scholar
  31. 31.
    O. T. O'Meara,Introduction to Quadratic Forms, Springer, Berlin-Heidelberg-New York (1973).Google Scholar
  32. 32.
    J. Milnor and D. Husemoller,Symmetric Bilinear Forms, Springer, Berlin-Heidelberg-New York (1973).Google Scholar
  33. 33.
    J. Oesterle, “Nombres de Tamagawa et groupes unipotents en characterstiquep,”Invent. Math. 78, No. 1, 13–88 (1984).MATHMathSciNetGoogle Scholar
  34. 34.
    T. Ono, “Sur une propriété arithmétique des groupes commutatifs,”Bull. Soc. Math. France,85, 307–323 (1957).MATHMathSciNetGoogle Scholar
  35. 35.
    T. Ono, “Arithmetic of algebraic tori,”Ann. Math.,74, 101–139 (1961).MATHGoogle Scholar
  36. 36.
    T. Ono, “On the Tamagawa number of algebraic tori,”Ann. Math.,78, 47–73 (1963).MATHGoogle Scholar
  37. 37.
    T. Ono, “On the relative theory of Tamagawa numbers,”Ann. Math.,82, 88–111 (1965).MATHGoogle Scholar
  38. 38.
    T. Ono, “On some class number relations for Galois extensions,”Nagoya Math. J.,107, 121–133 (1987).MATHMathSciNetGoogle Scholar
  39. 39.
    J.-J. Sansuc, “Groupe de Brauer et arithmetique des groupes algebriques linéaires sur un corps de nombres,”J. Reine Angew. Math. 327, 12–80 (1981).MATHMathSciNetGoogle Scholar
  40. 40.
    B. Schmithals, “Kapitulation der Idealklassen und Einheitenstruktur in Zahlkörpern,”J. Reine Angew. Math.,385, 43–60 (1985).MathSciNetGoogle Scholar
  41. 41.
    J.-P. Serre,Lie Algebras and Lie Groups. Algèbres de Lie Semisimples Complexes, Benjamin, New York-Amsterdam (1963, 1966).Google Scholar
  42. 42.
    J.-P. Serre,Cours d'arithmétique, Paris (1973).Google Scholar
  43. 43.
    R. Steinberg,Lectures on Chevalley Groups, Yale University (1967).Google Scholar
  44. 44.
    A. Trojan, “The integral extension of quadratic forms over local fields,”Canad. J. Math.,18, 920–942 (1966).MATHMathSciNetGoogle Scholar
  45. 45.
    A. Weil,Adeles and Algebraic Groups, The Institute for Advanced Study, Princeton, New Jersey (1961)Google Scholar
  46. 46.
    A. Weil,Basic Number Theory, Springer, Berlin-Heidelberg-New York (1967).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • V. E. Voskresenskii

There are no affiliations available

Personalised recommendations