Mathematische Annalen

, Volume 247, Issue 1, pp 1–20 | Cite as

On the resolution of cusp singularities and the Shintani decomposition in totally real cubic number fields

  • E. Thomas
  • A. T. Vasquez
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ash, A., Mumford, D., Rapoport, M., Tai, Y.: Smooth compactifications of locally symmetric varieties. Brookline, Mass.: Mathematical Sciences Press 1975Google Scholar
  2. 2.
    Berwick, W.H.H.: Algebraic number fields with two independent units, Proc. London Math. Soc. (2)34, 360–78 (1932)Google Scholar
  3. 3.
    Cohn, H.: Formal ring of a cubíc solid angle. J. Number Theory10, 135–50 (1978)Google Scholar
  4. 4.
    Delone, B.N., Faddeev, D.K.: The theory of irrationalities of the third degree. Translations of Mathematical Monographs, Vol. 10. Providence, R.I.: American Mathematical Society 1964Google Scholar
  5. 5.
    Ehlers, F.: Eine Klasse komplexer Mannigfaltigkeiten und die Auflösung einiger isolierter Singularitäten. Math. Ann.218, 127–56 (1975)Google Scholar
  6. 6.
    Fujiki, A.: On resolutions of cyclic quotient singularities. Publ. RIMS, Kyoto Univ.10, 293–328 (1974)Google Scholar
  7. 7.
    Hasse, H.: Arithmetische Bestimmung von Grundeinheit und Klassenzahl in zyklischen kubischen und biquadratischen Zahlkörpern. Math. Abh.3, 289–379 (1975)Google Scholar
  8. 8.
    Hirzebruch, F.: The Hilbert modular group, resolution of the singularities at the cusps and related problems. Sem. Bourbaki no. 396 1970/71Google Scholar
  9. 9.
    Hirzebruch, F.: Hilbert Modular surfaces. L'Enseignement Math.19, 183–281 (1974)Google Scholar
  10. 9a.
    Nagell, T.: Zur Arithmetik der Polynome. Abh. Math. Sem. Univ. Hamburg1, 179–194 (1922)Google Scholar
  11. 10.
    Nakamula, K.: On a fundamental domain forR +3. J. Fac. Sci. University of Tokyo, Sect. 1A, Vol. 24 701–13 (1977)Google Scholar
  12. 11.
    Satake, I.: On the arithmetic of tube domains. Bull. Am. Math. Soc.79, 1076–94 (1973)Google Scholar
  13. 12.
    Satake, I.: On the blowing-ups of Hilbert modular surfaces. J. Fac. Sci. University of Tokyo, Sect. 1A24, 221–9 (1977)Google Scholar
  14. 13.
    Shintani, T.: On evaluation of zeta functions of totally real algebraic number fields at non-positive integers. J. Fac. Sci. University of Tokyo, Sect. 1A23, 393–417 (1976)Google Scholar
  15. 14.
    Stender, H.J.: Einheiten für eine allgemeine Klasse total reeller algebraischer Zahlkörper. J. Reine Angew. Math.257, 151–78 (1972)Google Scholar
  16. 15.
    Thomas, E.: Fundamental units for orders in certain cubic number fields. J. Reine Angew. Math.310, 33–55 (1979)Google Scholar
  17. 16.
    Zagier, D.: A Kronecker limit formula for real quadratic fields. Math. Ann.213, 153–184 (1975)Google Scholar
  18. 17.
    Zagier, D.: Valeurs des fonctions zeta des corps quadratiques reel aux entiers negatifs. Asterisque, no. 41–42, Soc. Math. de France, 1977Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • E. Thomas
    • 1
  • A. T. Vasquez
    • 2
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Graduate SchoolCUNYNew YorkUSA

Personalised recommendations