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arXiv · 1510.05795

Explicit computations of Hida families via overconvergent modular symbols

Evan P. Dummit·Márton Hablicsek·Robert Harron·Lalit Jain·Robert Pollack·Daniel Ross
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Abstract

In [Pollack-Stevens 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-Pollack 2006, Trifkovi\'c 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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Evan P. Dummit, Márton Hablicsek, Robert Harron, Lalit Jain, Robert Pollack, Daniel Ross. 2015-10-20. Explicit computations of Hida families via overconvergent modular symbols. https://arxiv.org/abs/1510.05795

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