Dedekind sums and noncongruence subgroups of the Hecke groups $G(\sqrt {2})$ and $G(\sqrt {3})$
HTML articles powered by AMS MathViewer
- by L. Alayne Parson PDF
- Proc. Amer. Math. Soc. 57 (1976), 194-196 Request permission
Abstract:
An example is given of a character ${\chi _r}$ on a subgroup of $G(\sqrt 2 )$ or $G(\sqrt 3 )$ such that the kernel of ${\chi _r}$ is of finite index in $G(\sqrt 2 )$ or $G(\sqrt 3 )$ but is not a congruence subgroup.References
- J. I. Hutchinson, On a class of automorphic functions, Trans. Amer. Math. Soc. 3 (1902), no.Β 1, 1β11. MR 1500582, DOI 10.1090/S0002-9947-1902-1500582-5
- Marvin Isadore Knopp, Determination of certain roots of unity in the theory of automorphic forms of dimension zero, Duke Math. J. 27 (1960), 497β506. MR 114795
- Armin Leutbecher, Γber die Heckeschen Gruppen ${\mathfrak {G}}(\lambda )$, Abh. Math. Sem. Univ. Hamburg 31 (1967), 199β205 (German). MR 228438, DOI 10.1007/BF02992399
- L. Alayne Parson, Generalized Kloosterman sums and the Fourier coefficients of cusp forms, Trans. Amer. Math. Soc. 217 (1976), 329β350. MR 412112, DOI 10.1090/S0002-9947-1976-0412112-8
- L. Alayne Parson, Non-congruence subgroups for the Hecke groups $G(\surd 2)$ and $G(\surd 3)$, Illinois J. Math. 19 (1975), 79β86. MR 376538
- John Roderick Smart, Parametrization of automorphic forms for the Hecke groups $G(\surd 2)$ and $G(\surd 3)$, Duke Math. J. 31 (1964), 395β403. MR 165101
- Klaus Wohlfahrt, Γber Dedekindsche Summen und Untergruppen der Modulgruppe, Abh. Math. Sem. Univ. Hamburg 23 (1959), 5β10 (German). MR 102559, DOI 10.1007/BF02941021
- John Wesley Young, On the group of sign $(0,3;2,4,\infty )$ and the functions belonging to it, Trans. Amer. Math. Soc. 5 (1904), no.Β 1, 81β104. MR 1500662, DOI 10.1090/S0002-9947-1904-1500662-6
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 57 (1976), 194-196
- MSC: Primary 10D05; Secondary 20H10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0409363-0
- MathSciNet review: 0409363