Explicit computations of Hida families via overconvergent modular symbols
Dummit, E. P.
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Citation (published version)EP Dummit, M Hablicsek, R Harron, L Jain, R Pollack, D Ross. 2016. "Explicit computations of Hida families via overconvergent modular symbols." Research in Number Theory, Volume 2, Issue 1, pp. 25 - 25. https://doi.org/10.1007/s40993-016-0052-8
In 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.