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arXiv · 1908.00091

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

Daniel Barrera Salazar·Santiago Molina Blanco
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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.

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Daniel Barrera Salazar, Santiago Molina Blanco. 2019-07-31. Triple product p-adic L-functions for Shimura curves over totally real number fields. https://arxiv.org/abs/1908.00091

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