Jump to ContentJump to Main Navigation
Computational Aspects of Modular Forms and Galois RepresentationsHow One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)$
Users without a subscription are not able to see the full content.

Bas Edixhoven and Jean-Marc Couveignes

Print publication date: 2011

Print ISBN-13: 9780691142012

Published to University Press Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142012.001.0001

Show Summary Details
Page of
date: 13 December 2017

Approximating Vf over the complex numbers

Approximating Vf over the complex numbers

Chapter:
(p.257) Chapter Twelve Approximating Vf over the complex numbers
Source:
Computational Aspects of Modular Forms and Galois Representations
Author(s):

Jean-Marc Couveignes

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142012.003.0012

This chapter addresses the problem of computing torsion divisors on modular curves with an application to the explicit calculation of modular representations. The final result of the chapter is Theorem 12.14.1 (approximating Vsubscript f). It identifies two differences between this Theorem 12.14.1 and Theorem 12.10.7. First, it claims that it can separate the cuspidal and the finite part of Qₓ. Second, it returns algebraic coordinates b and x for the points Qsubscript x,n rather than analytic ones.

Keywords:   modular forms, torsion divisors, modular curves, modular representation

University Press Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs, and if you can't find the answer there, please contact us .