Dedekind sums and noncongruence subgroups of the Hecke groups 𝐺(√2) and 𝐺(√3)

Parson, L. Alayne

doi:10.1090/S0002-9939-1976-0409363-0

Dedekind sums and noncongruence subgroups of the Hecke groups $G(\sqrt {2})$ and $G(\sqrt {3})$
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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. 1, 1–11. 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), 497–506. MR 114795
Armin Leutbecher, Über die Heckeschen Gruppen ${\mathfrak {G}}(\lambda )$, Abh. Math. Sem. Univ. Hamburg 31 (1967), 199–205 (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), 329–350. 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), 79–86. 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), 395–403. MR 165101
Klaus Wohlfahrt, Über Dedekindsche Summen und Untergruppen der Modulgruppe, Abh. Math. Sem. Univ. Hamburg 23 (1959), 5–10 (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. 1, 81–104. MR 1500662, DOI 10.1090/S0002-9947-1904-1500662-6