Regular maps and principal congruence subgroups of Hecke groups

Galois Orbits of Principal Congruence Hecke Curves

We show that the natural action of the absolute Galois group on the ideals defining principal congruence subgroups of certain nonarithmetic Fuchsian triangle groups is compatible with its action on the algebraic curves that these congruence groups uniformize.

The Riemann Zeta-Function and Hecke Congruence Subgroups. II

which was scantly touched on in [9]. We shall proceed with an arbitrary A to a considerable extent but later restrict ourselves to the situation where αn is supported by the set of square-free integers. This is solely to avoid certain technical complexities pertaining to Kloosterman sums associated with Hecke congruence subgroups which do not appear particularly worth dealing with thoroughly, f...

Congruence Subgroups of Groups Commensurable with PSL

One-Cusped Congruence Subgroups of Bianchi Groups

We show that there are only finitely many maximal congruence subgroups of the Bianchi groups such that the quotient by H has only one cusp.

Cuspidal Cohomology for Principal Congruence Subgroups of Gl(3, Z)

The cohomology of arithmetic groups is made up of two pieces, the cuspidal and noncuspidal parts. Within the cuspidal cohomology is a subspace— the /-cuspidal cohomology—spanned by the classes that generate representations of the associated finite Lie group which are cuspidal in the sense of finite Lie group theory. Few concrete examples of /-cuspidal cohomology have been computed geometrically...