Big Heegner points and special values of L-series

2014/12/22 by Francesc Castella, Matteo Longo, Castella, Francesc +1 · 4 citations
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1412.7071

openalex publication_date 2014/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citeLV, Howard's construction of big Heegner points on modular curves was extended to general Shimura curves over the rationals. In this paper, we relate the higher weight specializations of the big Heegner points of loc.cit. in the definite setting to certain higher weight analogues of the Bertolini-Darmon theta elements. As a consequence of this relation, some of the conjectures formulated in \citeLV are deduced from recent results of Chida-Hsieh.

Citations

• Quaternion algebras, Heegner points and the arithmetic of Hida families

Cited by

• Quaternionic big Heegner points over totally real fields
• On quaternionic ordinary families of modular forms and p-adic L-functions
• Quaternionic families of Heegner points and p-adic L-functions
• Diagonal cycles and anticyclotomic twists of modular forms at inert primes

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