Triple product p-adic L-functions for finite slope families and a p-adic Gross-Zagier formula

2024/03/27 by Ting-Han Huang, Huang, Ting-Han
Mathematics · #11F12 #11G05 #11G35 #11G40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2403.18620

openalex publication_date 2024/03/27 · openalex created_date 2024/03/29 · openalex updated_date 2026/07/28

Abstract

In this paper, we generalize two results of H. Darmon and V. Rotger on triple product p-adic L-functions associated with Hida families to finite slope families. We first prove a p-adic Gross-Zagier formula, then demonstrate an application to a special case of the equivariant Birch and Swinnerton-Dyer conjecture for supersingular elliptic curves.

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