Commensurability classes and volumes of hyperbolic 3-manifolds
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 8 (1981) no. 1, p. 1-33 
@article{ASNSP_1981_4_8_1_1_0,
     author = {Borel, Armand},
     title = {Commensurability classes and volumes of hyperbolic 3-manifolds},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 8},
     number = {1},
     year = {1981},
     pages = {1-33},
     zbl = {0473.57003},
     mrnumber = {616899},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1981_4_8_1_1_0}
}

Borel, A. Commensurability classes and volumes of hyperbolic 3-manifolds. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 4, Volume 8 (1981) no. 1, pp. 1-33. http://www.numdam.org/item/ASNSP_1981_4_8_1_1_0/

[1] R. Baer, The group of motions of a two-dimensional elliptic plane, Compositio Math., 9 (1951), pp. 241-288. | Numdam | MR 48051 | Zbl 0045.10001

[2] A. Borel, Density and maximality of arithmetic subgroups, J. Reine Angew. Math., 224 (1966), pp. 78-89. | MR 205999 | Zbl 0158.03105

[3] Z.I. Borevich - I.R. Shafarevich, Number Theory, Academic Press, New York, 1966. | MR 195803 | Zbl 0145.04902

[4] M. Deuring, Algebren, Erg. d. Math. u. i. Grenzgeb. 4, Springer Verlag, 1935. | JFM 61.0118.01 | MR 228526 | Zbl 0011.19801

[5] M. Eichler, Ueber die Idealtheorie hyperkomplexer Systeme, Math. Z., 43 (1938), pp. 481-494. | JFM 64.0085.01 | MR 1545733 | Zbl 0018.20201

[6] R. Fricke, Ueber den aritmetischen Charaker der zu den Verzweigungen (2, 3, 7) und (2, 4, 7) gehörenden Dreicksfunctionen, Math. Ann., 41 (1893), pp. 443-468. | JFM 24.0395.01 | MR 1510754

[7] R. Fricke - F. Klein, Vorlesungen über die Theorie der automorphen Functionen, Band I, B. G. Teubner, Leipzig, 1893. | JFM 28.0334.01

[8] H.J. Godwin, On quartic fields with signature one with small discriminants, Quart. J. Math. Oxford, 8 (1957), pp. 214-222. | MR 97375 | Zbl 0079.05704

[9] H. Helling, Bestimmung der Kommensurabilitätsklasse der Hilbertschen Modulgruppe, Math. Z., 92 (1966), pp. 269-280. | MR 228437 | Zbl 0143.30601

[10] N. Iwahori - H. Matsumoto, On some Bruhat decompositions and the structure of the Hecke rings of p-adic Chevalley groups, Publ. Math. I.H.E.S., 25 (1965), pp. 237-280. | Numdam | MR 185016 | Zbl 0228.20015

[11] H. Jacquet - R. Langlands, Automorphic forms on GL(2), Lecture Notes in Mathematics 114, Springer-Verlag 1970. | MR 401654 | Zbl 0236.12010

[12] K. Takeuchi, Commensurability classes of arithmetic triangle groups, J. Fac. Sci. Univ. Tokyo, 24 (1977), pp. 201-212. | MR 463116 | Zbl 0365.20055

[13] G.A. Margoulis, Discrete groups of isometries of manifolds of nonpositive curvature, Proc. Int. Congress Math. 1974, Vancouver, Vol. 2, pp. 21-34.

[14] J. Mayer, Die absolut-kleinsten Diskriminanten der biquadratischen Zahlkörper, Sitzungsber. Akad. Wiss. Wien(IIA), 138 (1929), pp. 733-742. | JFM 55.0104.05

[15] A.M. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math., 29 (1975), pp. 275-286. | MR 376613 | Zbl 0306.12005

[16] T. Ono, On algebraic groups and discontinuous subgroups, Nagoya Math. J., 27 (1966), pp. 297-322. | MR 199193 | Zbl 0166.29802

[17] M.S. Raghunathan, Discrete subgroups of Lie groups, Erg. d. Math. u. i. Grenzgeb., 68, Springer Verlag, 1972. | MR 507234 | Zbl 0254.22005

[18] J. Rohlfs, Ueber maximale arithmetisch definierte Gruppen, Math. Ann., 234 (1978), pp. 239-252. | MR 498975 | Zbl 0384.20038

[19] J. Rohlfs, Die maximalen arithmetisch definierten Untergruppen zerfallender einfacher Gruppen, preprint. | MR 553253

[20] J-P. Serre, Cohomologie des groupes discrets, in Prospects in Math., Annals Math. Studies, 70, Princeton U. Press 1970, pp. 77-168. | MR 385006 | Zbl 0235.22020

[21] J-P. Serre, Arbres, amalgames, SL2, Astérisque, 46 (1977), Soc. Math. France. | MR 476875 | Zbl 0369.20013

[22] H. Shimizu, On zeta functions of quaternion algebras, Ann. of Math., (2) 81 (1965), pp. 166-193. | MR 171771 | Zbl 0201.37903

[23] C.L. Siegel, The volume of the fundamental domain for some infinite groups, Trans. A.M.S., 39 (1936), pp. 209-218. | JFM 62.0137.01 | MR 1501843 | Zbl 0013.24901

[24] W. Thurston, The geometry and topology of 3-manifolds, mimeographed Notes, Princeton University.

[25] J. Tits, Travaux de Margulis sur les sous-groupes discrets de groupes de Lie, Sém. Bourbaki, Exp. 482, Février 1976, Springer L.N., 567, pp. 174-190. | Numdam | MR 492073 | Zbl 0346.22011

[26] H.C. Wang, On a maximality property of discrete subgroups with fundamental domain of finite measure, Amer. J. Math., 89 (1967), pp. 124-132. | MR 207895 | Zbl 0152.01002

[27] H.C. Wang, Topics on totally discontinuous groups, in Symmetric spaces, W. Boothby ed., M. Dekker 1972, pp. 460-487. | MR 414787 | Zbl 0232.22018

[28] A. Weil, Basic Number Theory, Grund. Math. Wiss., 144, Springer-Verlag 1967. | MR 234930 | Zbl 0176.33601

[29] A. Weil, Adeles and algebraic groups, Notes by M. Demazure and T. Ono, The Institute for Advanced Study, 1961. | MR 670072

[30] B. Weisfeiler, On abstract monomorphisms of k-forms of PGL(2), J. Algebra, 57 (1979), pp. 522-543. | MR 533812 | Zbl 0406.20035