The Gross-Zagier formula on singular moduli for Shimura curves

2025/09/15 by Andrew Phillips, Phillips, Andrew · 1 voice
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.2509.11553

openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.

Discussions

• The Gross-Zagier formula on singular moduli for Shimura curves - By arXiv https://arxiv.org/abs/2509.11553 This paper generalizes the Gross-Zagier formula to Shimura curves, calculating the intersecti [bsky, 1 points, 0 comments]

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