Modular forms, L-functions and p-adic interpolation

Giovanni Rosso (University of Cambridge)

Frank Adams 1,

We shall recall what a modular form is and which objects (Galois representation and L-function) can be associated to it and then concentrate on the values of this L-function at certain positive integers. We shall see under which conditions on the modular form these values vary p-adically, where p is a fixed prime number, and can be used to define a p-adic L-function. We shall conclude stating a conjecture on the behavior of p-adic L-function when trivial zeros appear and how this conjecture can be approached, both for modular forms and other automorphic forms.
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