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

2019/07/31 by Daniel Barrera Salazar, Salazar, Daniel Barrera, Santiago Molina Blanco +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1908.00091

openalex publication_date 2019/07/31 · openalex created_date 2019/08/13 · arxiv created 2019/09/23 · arxiv updated 2019/09/24 · openalex updated_date 2026/07/28

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.

Citations

• On a conjecture of Jacquet

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