标题： L-函数的多重值模形式 显示英文标题

标题： Valeurs multiples de fonctions L de formes modulaires

摘要： 本博士论文研究了数论中两个著名成果集合之间的重叠部分：由 Eichler、Shimura 和 Manin 发展的模形式的周期与周期多项式理论及其由 Köhnen 和 Zagier 扩展的部分，以及 Euler 开创并由过去二十年众多作者研究的“多重泽塔值”(MZV) 理论。 Manin 将“多重 L 值”(MLV) 引入，从而将这两个理论联系起来。 我们提议研究这些数字族，并着重研究它们之间的关系，推广 Eichler-Shimura-Manin 关系，还将其中一些 MLV 与 MZV 联系起来。 显示英文摘要

摘要： 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.