Explicit computations of Hida families via overconvergent modular\n symbols

2015/10/20 by Evan P. Dummit, Márton Hablicsek, Dummit, Evan P. +9
Mathematics · #11F33 #11F67 #11F85 #11R23 #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.1510.05795

openalex publication_date 2015/10/20 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28

Abstract

In [Pollack-Stevens 2011], efficient algorithms are given to compute with\noverconvergent modular symbols. These algorithms then allow for the fast\ncomputation of p-adic L-functions and have further been applied to compute\nrational points on elliptic curves (e.g. [Darmon-Pollack 2006, Trifkovi 'c\n2006]). In this paper, we generalize these algorithms to the case of families\nof overconvergent modular symbols. As a consequence, we can compute p-adic\nfamilies of Hecke-eigenvalues, two-variable p-adic L-functions,\nL-invariants, as well as the shape and structure of ordinary Hida-Hecke\nalgebras.\n

Related

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• Triple product p-adic L-functions associated to finite slope p-adic families of modular forms, with an appendix by Eric Urban