2023/01/21 by Håvard Damm-Johnsen, Damm-Johnsen, Håvard · 1 citation
Mathematics · #11F33 #11R42 #11Y40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2301.08977
openalex publication_date 2023/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In recent work, Darmon, Pozzi and Vonk explicitly construct a modular form whose spectral coefficients are p-adic logarithms of Gross-Stark units and Stark-Heegner points. Here we describe how this construction gives rise to a practical algorithm for explicitly computing these logarithms to specified precision, and how to recover the exact values of the Gross-Stark units and Stark-Heegner points from them. Key tools are overconvergent modular forms, reduction theory of quadratic forms and Newton polygons. As an application, we tabulate Brumer-Stark units in narrow Hilbert class fields of real quadratic fields with discriminants up to 10000, for primes less than 20, as well as Stark-Heegner points on elliptic curves.