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On classical weight one forms in Hida families

Mladen Dimitrov, Eknath Ghate (2012)

Journal de Théorie des Nombres de Bordeaux

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.

On computing quaternion quotient graphs for function fields

Gebhard Böckle, Ralf Butenuth (2012)

Journal de Théorie des Nombres de Bordeaux

Let Λ be a maximal 𝔽 q [ T ] -order in a division quaternion algebra over 𝔽 q ( T ) 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 Λ * on the Bruhat-Tits tree 𝒯 associated to PGL 2 ( 𝔽 q ( ( 1 / T ) ) ) . 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 Λ * in terms of generators and relations. Moreover we determine an upper bound...

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