Valeurs multiples de fonctions L de formes modulaires

Abstract

This doctoral thesis studies the overlap between two well-known collections of results in number theory: the theory of periods and period polynomials of modular forms as developed by Eichler, Shimura and Manin and its extensions by K\"ohnen and Zagier, and the theory of 'multiple zeta values' (MZV's) as initied by Euler and studied by many authors in the last two decades. These two theories had been linked by Manin, who introduced 'multiple L-values' (MLV's). We propose to study those families of number and especially the relations among them, generalizing the Eichler-Shimura-Manin relations, and also linked some of those MLV's to MZV's.