La matrice de logarithme en termes de chiffres p-adiques

Abstract

We give a new description of the logarithm matrix of a modular form in terms of distributions, generalizing the work of Dion and Lei for the case \(a_p=0\). What allows us to include the case \(a_p\ne 0\) is a new definition, that of a distribution matrix, and the characterization of this matrix by p-adic digits. One can apply these methods to the corresponding case of distributions in multiple variables.