Triple product p-adic L-functions
We consider three Coleman families of modular forms and we would like to construct a p-adic L-function interpolating the algebraic part of central values of the triple product L-function attached to these families and classical weights.
p-adic Hodge theory (II)
The spaces of nearly holomorphic and nearly overconvergent modular forms
Rigid analytic modular forms
Rigid analytic modular forms are p-adic analogues of the classical holomorphic modular forms.
Values at CM points of nearly rigid modular forms
I will explain the main result of C.Franc’s thesis.
Beilinson-Flach classes
A rigid analytic approach to singular moduli (I)
The theory of complex multiplication gives a very satisfactory method for constructing abelian extensions of imaginary quadratic fields, by means of the j-invariant attached to certain CM elliptic curves, and some related invariants.
The eigencurve at irregular weight one Eisenstein points
In 1972, Serre observed that the Hecke eigenvalues of Eisenstein series can be p-adically interpolated. In other words, Eisenstein series can be viewed as a p-adic family parametrized by the weight.
A rigid analytic approach to singular moduli (II)
The theory of complex multiplication gives a very satisfactory method for constructing abelian extensions of imaginary quadratic fields, by means of the j-invariant attached to certain CM elliptic curves, and some related invariants.
Picard modular surfaces and families of automorphic forms (I)
p-adic families of modular forms as constructed first by Hida and in greater generality by Coleman and their generalizations are a great tool in modern number theory that appears in different parts of the Langlands program.