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Macbeath's curve and the modular group
Published online by Cambridge University Press: 18 May 2009
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The theory of algebraic curves associated with subgroups of finite index in the modular group Γ is highly developed for such subgroups of Γ as may be defined by means of congruences in the ring ℤ of rational integers. The situation in he case of non-congruence subgroups of Γ, on the other hand, is drastically different. It reduces to a few isolated examples, two of which may be found in [12]. Related research by A. O. L. Atkin and H. P. F. Swinnerton-Dyer began in [1].
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REFERENCES
1.Atkin, A. O. L. and Swinnerton-Dyer, H. P. F., Modular forms on non-congruence subgroups, Proc. Sympos. Pure Math. Vol. XIX (A.M.S., 1971), 1–25.Google Scholar
2.Cohen, J. M., On Hurwitz extensions by PSL(2,7), Math. Proc. Cambridge Philos. Soc. 86 (1979), 395–400.CrossRefGoogle Scholar
3.Cohen, J. M., On covering Klein's curve and generating projective groups. The Geometric Vein in The Coxeter Festschrift, (Springer-Verlag, 1982), 511–518.Google Scholar
4.Macbeath, A. M., On a curve of genus 7, Proc. London Math. Soc. 15 (1965), 527–542.CrossRefGoogle Scholar
5.Millington, M. H., On cycloidal subgroups of the modular group, Proc. London Math. Soc. 19 (1969), 164–176.CrossRefGoogle Scholar
6.Millington, M. H., Subgroups of the classical modular group, J. London Math. Soc. 1 (1969), 351–357.CrossRefGoogle Scholar
7.Sinkov, A., On the group-defining relations (2, 3, 7; p), Ann. of Math. 38 (1937), 577–584.CrossRefGoogle Scholar
8.Tate, J., Algorithm for determining the type of a singular Fiber in an Elliptic Pencil in Modular functions of one variable IV, LNM 476 (1975), 33–52.Google Scholar
9.Wohlfahrt, K., An extension of F. Klein's level concept, Illinois J. Math. 8 (1964), 529–535.CrossRefGoogle Scholar
10.Wohlfahrt, K., Zur Struktur der rationalen Modulgruppe, Math. Ann. 174 (1967), 79–99.CrossRefGoogle Scholar
11.Wohlfahrt, K., On some representations of SL(2, Z), Illinois J. Math. 15 (1971), 144–149.CrossRefGoogle Scholar
12.Wohlfahrt, K., Über die rationalen Punkte dreier elliptischer Kurven, J. Reine Angew. Math. 268/269 (1974), 348–359.Google Scholar
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