Exposés
Hecke grossencharacters
Atelier Pari/GP, janvier 2021
A very basic explaination of Hecke grossencharacters, with examples.
Computing periods of algebraic curves
Atelier Pari/GP, janvier 2019
I explain the strategy used to compute periods of curves to high accuracy.
Calcul numérique de l'applications d'Abel-Jacobi
Journées ANR FastRelax, juin 2018
I explain the strategy used to compute periods of curves to high accuracy. See hcperiods paper.
Building L functions
Atelier Pari/GP, juin 2017
I show how one can use approximate functional equations to compute Dirichlet coefficients of L functions without knowledge of the underlying arithmetic object. (talk already given in Bristol)
Periods of hyperelliptic curves
Séminaire à Bristol, mai 2017
I explain the strategy used to compute periods of curves to high accuracy. See hcperiods paper.
Numerical integration and the DE method
Colloquium à Oldenburg, décembre 2016
An introduction to the Double Exponential integration method (with a quick and unfair comparison with Gauss-Legendre).
New features of Pari/GP
Conférence à Oldenburg, june 2017
Périodes de courbes superelliptiques
Séminaire Evry, novembre 2016
On présente un algorithme de calcul à grande précision des périodes complexes des courbes de la forme y^n = f(x), qui permet de traiter des courbes de très grand genre.
L functions in Pari/GP
Conférence ICMS Berlin, july 2016
A package to compute with general L functions now available in the Pari/GP computer algebra system. L functions of all classical objects already in Pari/GP are available (Dirichlet and Hecke characters, elliptic curves, some modular forms), but the package is meant to handle L functions of any kind. I explain the methods used and their limits (joint work with B. Allombert, K. Belabas, and H. Cohen).
Using the approximate functional equation to build L functions
Séminaire Bristol, february 2016
Some computations and methods to locate or build analytic L functions from their Selberg data, using approximate functional equations.
L functions in Pari/GP
Conférence ICERM, november 2015
Short introduction to the L function package now available in Pari/GP (joint work with B. Allombert, K. Belabas, and H. Cohen).
Fast and rigorous evaluation of one gamma factor L functions
Conférence à Tianjin, july 2015
Description of an algorithm for computing with L functions, which is numerically rigorous for simple L functions, and some applications.
Computing periods of hyperelliptic curves
Séminaire à Oldenburg, january 2015
Brief presentation of the double-exponential method for numerical integration of complex fonction, and description of an algorithm to compute numerically the period matrix and the Abel-Jacobi map of (complex) hyperelliptic curves to arbitrary precision, based on this method. The complexity is quadratic in both the genus and the accuracy.
a L-functions package for Pari/GP
Atelier Pari/GP, january 2015
Work in progress of the L functions package.
Using approximate functional equations
Conférence à Trieste, september 2014
Some tricks to recover missing invariants of L functions using approximate functional equations.
Travaux
Intégration numérique et calculs de fonctions L
thèse (octobre 2010), directeur K. Belabas.
Étude de la méthode d'intégration double-exponentielle et application à l'étude d'algorithmes de calcul de fonctions L rigoureux.
Arbitrary precision computation of one gamma factor L functions
algorithme utilisé dans PariGP
Contributions
Arb
Une bibliothèque d'arithmétique grande précision,
mes contributions concernent les caractères de Dirichlet
et la transformée de Fourier discrète.
LMFDB
Base de données de fonctions L, formes modulaires
et bien d'autres objets de théorie des nombres.
Je participe au projet.
Pari/GP
Système de calcul pour la théorie des nombres, mes
contributions concernent les fonctions L et les
caractères de Hecke (coming soon).