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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)$
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Bas Edixhoven and Jean-Marc Couveignes

Print publication date: 2011

Print ISBN-13: 9780691142012

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142012.001.0001

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Introduction, main results, context

Introduction, main results, context

Chapter:
(p.1) Chapter One Introduction, main results, context
Source:
Computational Aspects of Modular Forms and Galois Representations
Author(s):

Bas Edixhoven

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142012.003.0001

This chapter provides an introduction to the subject, precise statements of the main results, and places these in a somewhat wider context. Topics discussed include statement of the main results, Schoof's algorithm, Schoof's algorithm described in terms of ètale cohomology, other cases where ètale cohomology can be used to construct polynomial time algorithms for counting rational points of varieties over finite fields, congruences for Ramanujan's tau-function, and comparison with p-adic methods.

Keywords:   modular forms, Schoof's algorithm, Ramanujan's tau-function, ètale cohomology, polynomial time algoriths, p-adic methods

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