Computational Arithmetic of Modular Forms (Course notes)
Number Theory
2018-09-14 v1
Abstract
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted student to implement it over any ring (such that a sufficient linear algebra theory is available in the chosen computer algebra system). The chosen approach is based on group cohomology and along the way the needed tools from homological algebra are provided.
Cite
@article{arxiv.1809.04645,
title = {Computational Arithmetic of Modular Forms (Course notes)},
author = {Gabor Wiese},
journal= {arXiv preprint arXiv:1809.04645},
year = {2018}
}
Comments
Refereed lecture notes, 82 pages. To appear in the proceedings volume: "Notes from the International Autumn School on Computational Number Theory: Izmir Institute of Technology 2017"