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Computations with modular forms and Galois representations

Johan Bosman

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0006
Subject:
Mathematics, Number Theory

This chapter discusses several aspects of the practical side of computing with modular forms and Galois representations. It starts by discussing computations with modular forms, and from there work ... More


Epilogue

Bas Edixhoven and Jean-Marc Couveignes (eds)

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0016
Subject:
Mathematics, Number Theory

This epilogue describes some work on generalizations and applications, as well as a direction of further research outside the context of modular forms. Theorems 14.1.1 and 15.2.1 will certainly be ... More


Polynomials for projective representations of level one forms

Johan Bosman

in Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.003.0007
Subject:
Mathematics, Number Theory

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 ... More


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