Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6414253 | Journal of Algebra | 2016 | 26 Pages |
Abstract
We study the arithmetic and geometry properties of the Hecke group Gq. In particular, we prove that Gq has a subgroup X of index d, genus g with vâ cusps, and Ï2 (resp. vri) conjugacy classes of elliptic elements that are conjugates of S (resp. Rq/ri) if and only if (i) 2gâ2+Ï2/2+âi=1kvri(1â1/ri)+vâ=d(1/2â1/q), and (ii) m0=4gâ4+Ï2+2vâ+âi=1kvri(2âq/ri)â¥0 is a multiple of qâ2. Note that if q is odd (resp. prime), then m0/(qâ2)âZ (resp. Nâª{0}) is a consequence of (i).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Cheng Lien Lang, Mong Lung Lang,