An Arithmetic-Geometric Method in the Study of the Subgroups of the Modular Group
From MaRDI portal
Publication:3991549
DOI10.2307/2374900zbMath0758.11024OpenAlexW2042460932MaRDI QIDQ3991549
Publication date: 28 June 1992
Published in: American Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2307/2374900
convex polygonmodular groupfundamental domainspecial polygonFarey symbolgeneralized Farey sequencesubgroups with free system of generators
Generators, relations, and presentations of groups (20F05) Structure of modular groups and generalizations; arithmetic groups (11F06) Farey sequences; the sequences (1^k, 2^k, dots) (11B57)
Related Items
On Rademacher's conjecture: congruence subgroups of genus zero of the modular group. ⋮ Arithmetic and geometry of the Hecke groups ⋮ A conjectural extension of Hecke's converse theorem ⋮ Some presentations for \overline{Γ}₀(𝑁) ⋮ On suborbital graphs for the extended modular group \(\widehat\Gamma\). ⋮ Distinct distances on hyperbolic surfaces ⋮ Lifts of projective congruence groups, II ⋮ Length spectra of the Hecke triangle groups ⋮ Independent generators for congruence subgroups of Hecke groups ⋮ Binary quadratic forms as dessins ⋮ Unnamed Item ⋮ Concentration of closed geodesics in the homology of modular curves ⋮ Small diameters and generators for arithmetic lattices in \(\mathrm{SL}_2 (\mathbb{R})\) and certain Ramanujan graphs ⋮ On fundamental domains for subgroups of isometries acting in \(\mathbb H^n\) ⋮ GENERALIZED PELL SEQUENCES RELATED TO THE EXTENDED GENERALIZED HECKE GROUPS ${\bar{H}}$ 3,q AND AN APPLICATION TO THE GROUP ${\bar{H}}$ 3,3 ⋮ Modular symbols and Petersson's product ⋮ Wohlfahrt's theorem for the Hecke group \(G_5\) ⋮ Noncongruence subgroups and Maass waveforms ⋮ On the Extended Hecke Group $\overline{H}(\lambda_5)$ ⋮ \(H\)-convex standard fundamental domain of a subgroup of a modular group ⋮ Moduli interpretations for noncongruence modular curves ⋮ Some normal subgroups of the extended Hecke groups \(\overline H(\lambda_p)\). ⋮ Computing presentations of Fuchsian groups via fat-graphs ⋮ From Farey symbols to generators for subgroups of finite index in integral group rings of finite groups ⋮ Subgroups of the hecke groups with small index ⋮ CONVEX STANDARD FUNDAMENTAL DOMAIN FOR SUBGROUPS OF HECKE GROUPS ⋮ Circuit complexity of knot states in Chern-Simons theory ⋮ Products of pairs of Dehn twists and maximal real Lefschetz fibrations ⋮ Finite subgroups of the extended modular group ⋮ The shape of the Ford domains for Γ₀(𝑁) ⋮ Normalisers of subgroups of the modular group