A Note on Link Complements and Arithmetic Groups.
A spectral proof of Rademacher's conjecture for congruence subgroups of the modular group.
A Symbolic Dynamics for Geodesics on Punctured Riemann Surfaces.
Addendum : Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups
An isomorphism between polynomial eigenfunctions of the transfer operator and the Eichler cohomology for modular groups.
Analogs of Δ(z) for triangular Shimura curves
We construct analogs of the classical Δ-function for quotients of the upper half plane 𝓗 by certain arithmetic triangle groups Γ coming from quaternion division algebras B. We also establish a relative integrality result concerning modular functions of the form Δ(αz)/Δ(z) for α in B⁺. We give two explicit examples at the end.
Arithmetic Fuchsian groups and the number of systoles.
Arithmetische Eigenschaften hyperbolischer Klassen elliptischer Modulgruppen.
Around the Borromean link.
This is a survey of some consequences of the fact that the fundamental group of the orbifold with singular set the Borromean link and isotropy cyclic of order 4 is a universal kleinian group.
Chebyshev polynomials and the modulary group of level p
Classical projective geometry and arithmetic groups.
Closed geodesics, periods and arithmetic of modular forms.
Co-fibered products of algebraic curves
We give examples of failure of the existence of co-fibered products in the category of algebraic curves.
Cohomology of arithmetic subgroups of SL3 at infinity.
Cohomology sets inside arithmetic groups
Commutator subgroups of the extended Hecke groups
Hecke groups are the discrete subgroups of generated by and . The commutator subgroup of (, denoted by , is studied in [2]. It was shown that is a free group of rank . Here the extended Hecke groups , obtained by adjoining to the generators of , are considered. The commutator subgroup of is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the case, the index of is changed by , in the case of , this number is either 4 for...
Computing fundamental domains for Fuchsian groups
We exhibit an algorithm to compute a Dirichlet domain for a Fuchsian group with cofinite area. As a consequence, we compute the invariants of , including an explicit finite presentation for .
Congruence subgroups associated to the Monster.
Congruence subgroups of groups commensurable with of genus 0 and 1.
Congruence subgroups of ) of genus less than or equal to 24.