This master s thesis is intended to give a presentation of the theory of congruences between the Fourier coecients of modular forms. In order to do that we introduce the reader to the basic theory of modular forms from the ...

We construct p-adic L-functions associated with triples of finite slope p-adic families of quaternionic automorphic eigenforms over totally real fields on Shimura curves. These results generalize a previous construction, ...

En aquesta tesi presentem les propietats principals de les superfícies modulars de Hilbert i les formes modulars associades. La més remarcable és que poden ser vistes com a varietats modulars associades al grup ortogonal ...

Modular forms are holomorphic functions defined on the complex upper half-plane which transform in a certain way under the action of a group of matrices. Alternatively, they can be thought of as differential forms on a ...

For any elliptic curve E defined over the rationals with complex multiplication (CM) and for every prime p, we describe the image of the mod p Galois representation attached to E. We deduce information about the field of ...

This article is devoted to the elliptic Stark conjecture formulated by Darmon (Forum Math Pi 3:e8, 2015), which proposes a formula for the transcendental part of a p-adic avatar of the leading term at s=1 of the Hasse–Weil–Artin ...