Arithmetic Fuchsian groups with signature (1; e)

Kisao TAKEUCHI

doi:10.2969/jmsj/03530381

Kisao TAKEUCHI

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JOURNAL FREE ACCESS

1983 Volume 35 Issue 3 Pages 381-407

DOI https://doi.org/10.2969/jmsj/03530381

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Published: 1983 Received: January 11, 1982 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 2) B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Trans. Math. Mono., 10, Amer. Math. Soc., 1964.
3) Gel'fand, Graev and Pyatetskii-Shapiro, Representation theory and automorphic functions, Acad. Sci. U. S. S. R., translated from Russian by K. A. Hirsch, 1969.
4) H. J. Godwin, Real quartic fields with small discriminant, J. London Math. Soc., 31 (1956), 478-485.
5) M. Hall, The theory of groups, Macmillan, New York, 1959.
6) G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford Univ. Press, 1975.
7) F. Klein and R. Fricke, Vorlesungen über die Theorie der automorphen Funktionen I,II, 1897.
8) D. H. Lehmer, An extended theory of Lucas functions, Ann. of Math., 31 (1930), 419-448, Teubner reprint, 1965.
9) J. Liang, On the integral basis of the maximal real subfield of a cyclotomic field, J. Reine Angew. Math., 286/287 (1976), 223-226.
10) L. J. Mordell, Diophantine equations, Academic Press, London, 1969.
11) A. Odlyzko, Unconditional bounds for discriminants, 1976, (A table of numerical values for the constants in a formula giving a lower bound of the discriminants of totally real algebraic number fields), preprint.
12) G. Pólya and G. Szegö, Problems and theorems in analysis II, Springer, New York, 1972.
13) N. Purzitsky and G. Rosenberger, Two generator Fuchsian groups of genus one, Math. Z., 128 (1972), 245-251.
14) H. Shimizu, On zeta functions of quaternion algebras, Ann. of Math., 81 (1965), 166-193.
15) K. Takeuchi, A remark on Fuchsian groups, Sci. Rep. Saitama Univ., 7 (1971), 1-3.
16) K. Takeuchi, A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan, 27 (1975), 600-612.
17) K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan, 29 (1977), 91-106.
18) K. Takeuchi, Commensurability classes of arithmetic triangle groups, J. Fac. Sci. Univ. Tokyo Sect. I, 24 (1977), 201-212.

Right : [2] B. N. Delone and D. K. Faddeev, The theory of irrationalities of the third degree, Trans. Math. Mono., 10, Amer. Math. Soc., 1964.
[3] Gel'fand, Graev and Pyatetskii-Shapiro, Representation theory and automorphic functions, Acad. Sci. U. S. S. R., translated from Russian by K. A. Hirsch, 1969.
[4] H. J. Godwin, Real quartic fields with small discriminant, J. London Math. Soc., 31 (1956), 478-485.
[5] M. Hall, The theory of groups, Macmillan, New York, 1959.
[6] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, Oxford Univ. Press, 1975.
[7] F. Klein and R. Fricke, Vorlesungen über die Theorie der automorphen Funktionen I,II, 1897.
[8] D. H. Lehmer, An extended theory of Lucas functions, Ann. of Math., 31 (1930), 419-448, Teubner reprint, 1965.
[9] J. Liang, On the integral basis of the maximal real subfield of a cyclotomic field, J. Reine Angew. Math., 286/287 (1976), 223-226.
[10] L. J. Mordell, Diophantine equations, Academic Press, London, 1969.
[11] A. Odlyzko, Unconditional bounds for discriminants, 1976, (A table of numerical values for the constants in a formula giving a lower bound of the discriminants of totally real algebraic number fields), preprint.
[12] G. Pólya and G. Szegö, Problems and theorems in analysis II, Springer, New York, 1972.
[13] N. Purzitsky and G. Rosenberger, Two generator Fuchsian groups of genus one, Math. Z., 128 (1972), 245-251.
[14] H. Shimizu, On zeta functions of quaternion algebras, Ann. of Math., 81 (1965), 166-193.
[15] K. Takeuchi, A remark on Fuchsian groups, Sci. Rep. Saitama Univ., 7 (1971), 1-3.
[16] K. Takeuchi, A characterization of arithmetic Fuchsian groups, J. Math. Soc. Japan, 27 (1975), 600-612.
[17] K. Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan, 29 (1977), 91-106.
[18] K. Takeuchi, Commensurability classes of arithmetic triangle groups, J. Fac. Sci. Univ. Tokyo Sect. I, 24 (1977), 201-212.

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