Subgroups of Some Fuchsian Groups Defined by Two Linear Congruences
نویسنده
چکیده
In this article we define a new family of subgroups of Fuchsian groups H( √ m), for a squarefree positive integer m, and calculate their index in H( √ m) and their parabolic class number. Moreover, we will show that the index of these subgroups is closely related to the solvability of a quadratic congruence x2 ≡ m(mod n) and the number of inequivalent solutions of a quadratic congruence x2 ≡ 1(mod n). Finally, we will show that the results obtained by Yilmaz and Keskin [Acta Math. Sin 25 (2005), 215–222] are immediate corollaries of one of the main theorems of this article.
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