On arithmetic Fuchsian groups and their characterizations
This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.
This is a small survey paper about connections between the arithmetic and geometric properties in the case of arithmetic Fuchsian groups.
We give precise estimates for the number of classical weight one specializations of a non-CM family of ordinary cuspidal eigenforms. We also provide examples to show how uniqueness fails with respect to membership of weight one forms in families.
Let be a maximal -order in a division quaternion algebra over which is split at the place . The present article gives an algorithm to compute a fundamental domain for the action of the group of units on the Bruhat-Tits tree associated to . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group in terms of generators and relations. Moreover we determine an upper bound...