Explicit computations of Hida families via overconvergent modular symbols
2016; Springer Science+Business Media; Volume: 2; Issue: 1 Linguagem: Inglês
10.1007/s40993-016-0052-8
ISSN2522-0160
AutoresEvan P. Dummit, Márton Hablicsek, Robert Harron, Lalit Jain, Robert Pollack, Daniel Ross,
Tópico(s)Analytic Number Theory Research
ResumoIn Pollack and Stevens (Ann Sci Éc Norm Supér 44(1):1–42, 2011), efficient algorithms are given to compute with overconvergent modular symbols. These algorithms then allow for the fast computation of p-adic L-functions and have further been applied to compute rational points on elliptic curves (e.g. Darmon and Pollack in Israel J Math 153:319–354, 2006, Trifkovic in Duke Math J 135(3):415–453, 2006). In this paper, we generalize these algorithms to the case of families of overconvergent modular symbols. As a consequence, we can compute p-adic families of Hecke-eigenvalues, two-variable p-adic L-functions, L-invariants, as well as the shape and structure of ordinary Hida–Hecke algebras.
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