Inventiones mathematicae

, Volume 86, Issue 3, pp 507–527

The smallest arithmetic hyperbolic three-orbifold

  • Ted Chinburg
  • Eduardo Friedman
Article

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References

  1. 1.
    Borel, A.: Commensurability classes and volumes of hyperbolic 3-manifolds. Ann. Sc. Norm. Super. Pisa, IV. Ser.VIII, 1–33 (1981)Google Scholar
  2. 2.
    Chinburg, T.: A small arithmetic hyperbolic 3-manifold. (To appear in the Proc. Am. Math. Soc.)Google Scholar
  3. 3.
    Chinburg, T.: Volumes of hyperbolic manifolds. J. Differ. Geom.18, 783–789 (1983)Google Scholar
  4. 4.
    Delone, B.N., Faddeev, D.K.: The theory of irrationalities of the third degree. A.M.S. Translations of Mathematical Monographs. Am. Math. Soc.,10 (1964)Google Scholar
  5. 5.
    Godwin, H.J.: On quartic fields with signature one and small discriminants. Q. J. Math. Oxford8, 214–222 (1957)Google Scholar
  6. 6.
    Lang, S.: Algebraic number theory. Reading, Mass.: Addison-Wesley, 1970Google Scholar
  7. 7.
    Margoulis, G.A.: Discrete groups of isometries of manifolds of nonpositive curvature. Proc. Int. Congr. Math. 1974, Vancouver,2, pp. 21–34Google Scholar
  8. 8.
    Martinet, J.: Petits discriminants des corps de nombres. In: Armitage, J.V. (ed.), Proceedings of the Journées Arithmétiques 1980. London Math. Soc. Lectures Notes series56, Cambridge University 1982, pp. 151–193Google Scholar
  9. 9.
    Meyerhoff, R.: A lower bound for the volumes of hyperbolic 3-manifolds. (Preprint 1983)Google Scholar
  10. 10.
    Meyerhoff, R.: The cusped hyperbolic 3-orbifold of minimum volume, research announcement. Bull. Am. Math. Soc.13, 154–156 (1985)Google Scholar
  11. 11.
    Odlyzko, A.M.: Some analytic estimates of class numbers and discriminants. Invent. Math.29, 275–286 (1975)Google Scholar
  12. 12.
    Odlyzko, A.M.: Lower bounds for discriminants of number fields II. Tohoku Math. J.29, 209–216 (1977)Google Scholar
  13. 13.
    Poitou, G.: Sur les petits discriminants. Sém. Delange-Pisot-Poitou (Théorie des nombres), exposé n. 6 (1976/77), pp. 6.01–6.18Google Scholar
  14. 14.
    Thurston, W.: The geometry and topology of 3-manifolds. Princeton University (preprint 1978)Google Scholar
  15. 15.
    Tits, J.: Travaux de Margulis sur les sous-groups discrets de groupes de Lie. Sém. Bourbaki. Springer Lect. Notes Math.567, 174–190 (1975/76)Google Scholar
  16. 16.
    Vignéras, M.F.: Arithmétique des algèbres de Quaternions. Springer Lect. Notes Math.800 (1980)Google Scholar
  17. 17.
    Wang, H.C.: Topic on totally discontinuous groups. In: Boothby, W. (ed.), Symmetric spaces, M. Dekker (1972), pp. 460–487Google Scholar
  18. 18.
    Weeks, J.: Hyperbolic structures on three-manifolds. Princeton Ph. D. thesis (1985)Google Scholar
  19. 19.
    Zimmert, R.: Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung. Invent. Math.62, 367–380 (1981)Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Ted Chinburg
    • 1
  • Eduardo Friedman
    • 1
  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA

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