Calculs effectifs de projections caract\'eristiques

TL;DR

This paper explicates Panchishkin's characteristic projection, detailing methods for effective computation and providing concrete examples to illustrate its application in constructing p-adic L-functions associated with modular forms.

Contribution

It clarifies Panchishkin's characteristic projection and offers practical computational techniques with illustrative examples for p-adic L-functions.

Findings

Explicit formulas for the characteristic projection.

Effective computational methods demonstrated.

Concrete examples of application provided.

Abstract

This article aims to make explicit the characteristic projection introduced by Panchishkin in "A new method of constructing p-adic L-functions associated with modular forms" (Moscow Mathematical Journal, 2002) and gives various results on how to calculate it effectively on a computer. It ends with concrete examples putting those ideas in application.