p-adic modular symbols attached to C. M. forms

In this thesis I study the relation between the (CM) Elliptic Construction and the Modular Construction of p-adic L-functions in two variables which interpolate special values of Hecke L-functions.; The first construction, due to N. Katz, and then R. Yager, is very explicit in terms of elliptic units using Iwasawa theory on formal groups. However, this construction does not imply the construction of a modular symbol for which the attached L-function is exactly this p-adic L-function.; The Modular construction, developed by R. Greenberg and G. Stevens, is more general. They attach to any Hida family of p-stabilized modular forms a p-adic modular symbol with values in the space of two variable p-adic distributions. However, this construction is not explicit.; We use p-adic methods to prove the existence of a modular symbol whose L-function is the Katz-Yager p-adic L-function.; The Weil representation constitutes a powerful tool in constructing modular forms. We use the Weil representation to construct a modular symbol with values in a big complex vector space, for which the attached L-function is the generating function of the special values of Hecke L-functions. This suggests the possibility of using the Weil representation to explicitly describe the p-adic modular symbol whose existence is established in this thesis.