2022/05/27 by Xinyi Yuan, Yuan, Xinyi
Mathematics · #11F67 #11G18 #14G40 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2205.13995
openalex publication_date 2022/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program.