On lambda-adic Saito-Kurokawa lifting and its application.

摘要

This thesis studies the p-adic nature of the Saito-Kurokawa lifting from a classic modular form to a Siegel modular form of degree 2, and its application on the algebraicity of central values. Applying Stevens' result on Λ-adic Shintani lifting, a Λ-adic Saito-Kurokawa lifting is constructed analogous to the construction of the classic Λ-adic Eisenstein Series. It is applied to construct a p-adic L-function on Sp2 x GL2. A conjecture on the specialization of this p-adic L-function is stated.