Bianchi modular symbols and p-adic L-functions

OVERCONVERGENT MODULAR SYMBOLS AND p-ADIC L-FUNCTIONS

Cet article est exploration constructive des rapports entre les symboles modulaires classique et les symboles modulaires p-adiques surconvergents. Plus précisément, on donne une preuve constructive d’un theorème de controle (Theoreme 1.1) du deuxiéme auteur [20]; ce theoréme preuve l’existence et l’unicité des “liftings propres” des symboles propres modulaires classiques de pente non-critique. ...

AUTOMORPHIC SYMBOLS, p-ADIC L-FUNCTIONS AND ORDINARY COHOMOLOGY OF HILBERT MODULAR VARIETIES

We introduce the notion of automorphic symbol generalizing the classical modular symbol and use it to attach very general p-adic L-functions to nearly ordinary Hilbert automorphic forms. Then we establish an exact control theorem for the p-adically completed cohomology of a Hilbert modular variety localized at a suitable nearly ordinary maximal ideal of the Hecke algebra. We also show its freen...

Modular Symbols and L-functions

As the rst non-overview lecture in this seminar, we will be setting up a lot of notation, getting comfortable working with modular symbols, and then hopefully discussing some of the major inputs which make the theory work. The rst half of the talk we will work through the example of the unique cusp form of weight two and level 11 on X0(11). In the second half, we will bring in the theoretical r...

The p-Adic L-Functions of Modular Elliptic Curves

The arithmetic theory of elliptic curves enters the new century with some of its major secrets intact. Most notably, the Birch and Swinnerton-Dyer conjecture, which relates the arithmetic of an elliptic curve to the analytic behaviour of its associated L-series, is still unproved in spite of important advances in the last decades, some of which are recalled in Chapter 1. In the 1960’s the pione...

p-ADIC PERIODS, p-ADIC L-FUNCTIONS, AND THE p-ADIC UNIFORMIZATION OF SHIMURA CURVES