References
Borel, A.: Commensurability classes and volumes of hyperbolic 3-manifolds. Ann. Sc. Norm. Super. Pisa, IV. Ser.VIII, 1–33 (1981)
Chinburg, T.: A small arithmetic hyperbolic 3-manifold. (To appear in the Proc. Am. Math. Soc.)
Chinburg, T.: Volumes of hyperbolic manifolds. J. Differ. Geom.18, 783–789 (1983)
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)
Godwin, H.J.: On quartic fields with signature one and small discriminants. Q. J. Math. Oxford8, 214–222 (1957)
Lang, S.: Algebraic number theory. Reading, Mass.: Addison-Wesley, 1970
Margoulis, G.A.: Discrete groups of isometries of manifolds of nonpositive curvature. Proc. Int. Congr. Math. 1974, Vancouver,2, pp. 21–34
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. 151–193
Meyerhoff, R.: A lower bound for the volumes of hyperbolic 3-manifolds. (Preprint 1983)
Meyerhoff, R.: The cusped hyperbolic 3-orbifold of minimum volume, research announcement. Bull. Am. Math. Soc.13, 154–156 (1985)
Odlyzko, A.M.: Some analytic estimates of class numbers and discriminants. Invent. Math.29, 275–286 (1975)
Odlyzko, A.M.: Lower bounds for discriminants of number fields II. Tohoku Math. J.29, 209–216 (1977)
Poitou, G.: Sur les petits discriminants. Sém. Delange-Pisot-Poitou (Théorie des nombres), exposé n. 6 (1976/77), pp. 6.01–6.18
Thurston, W.: The geometry and topology of 3-manifolds. Princeton University (preprint 1978)
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)
Vignéras, M.F.: Arithmétique des algèbres de Quaternions. Springer Lect. Notes Math.800 (1980)
Wang, H.C.: Topic on totally discontinuous groups. In: Boothby, W. (ed.), Symmetric spaces, M. Dekker (1972), pp. 460–487
Weeks, J.: Hyperbolic structures on three-manifolds. Princeton Ph. D. thesis (1985)
Zimmert, R.: Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung. Invent. Math.62, 367–380 (1981)
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Partially supported by NSF grant DMS-01503 and the Sloan Foundation
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Chinburg, T., Friedman, E. The smallest arithmetic hyperbolic three-orbifold. Invent Math 86, 507–527 (1986). https://doi.org/10.1007/BF01389265
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DOI: https://doi.org/10.1007/BF01389265