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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 University Press Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142012.001.0001

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date: 13 December 2017

Polynomials for projective representations of level one forms

Polynomials for projective representations of level one forms

Chapter:
(p.159) Chapter Seven Polynomials for projective representations of level one forms
Source:
Computational Aspects of Modular Forms and Galois Representations
Author(s):

Johan Bosman

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142012.003.0007

This chapter explicitly computes mod-ℓ Galois representations attached to modular forms. To be precise, it looks at cases with l ≤ 23, and the modular forms considered will be cusp forms of level 1 and weight up to 22. The chapter presents the result in terms of polynomials associated with the projectivized representations. As an application, it will improve a known result on Lehmer's nonvanishing conjecture for Ramanujan's tau function.

Keywords:   modular forms, Galois representations, cusp forms, polynomials, Ramanujan's tau function, Lehmer, nonvanishing conjecture

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