Triple product p-adic L-functions for Shimura curves over totally real number fields

Abstract

Let F be a totally real number field. Using a recent geometric approach developed by Andreatta and Iovita we construct several variables p-adic families of finite slope quaternionic automorphic forms over F. It is achieved by interpolating the modular sheaves defined over some auxiliary unitary Shimura curves. Secondly, we attach p-adic L-functions to triples of ordinary p-adic families of quaternionic automorphic eigenforms. This is done by relating trilinear periods to some trilinear products over unitary Shimura curves which can be interpolated adapting the work of Liu-Zhang-Zhang to our families.

References in corpus (6)

• Rankin--Eisenstein classes and explicit reciprocity laws
• On a conjecture of Jacquet
• Euler systems for Hilbert modular surfaces
• p-adic modular forms of non-integral weight over Shimura curves
• An analogue of the BGG resolution for locally analytic principal series
• The Birch and Swinnerton-Dyer Formula for Elliptic Curves of Analytic Rank One

Cited by in corpus (1)

• Finite slope Triple Product p-adic L-functions over totally real fields