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Computations with classical and p-adic modular forms

Part of: Computational number theory Arithmetic algebraic geometry Number theory

Published online by Cambridge University Press:  01 August 2011

Alan G. B. Lauder
Alan G. B. Lauder*
Affiliation:
Mathematical Institute, 24-29 St Giles, Oxford, United Kingdom (email: lauder@maths.ox.ac.uk)

Abstract

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We present p-adic algorithms for computing Hecke polynomials and Hecke eigenforms associated to spaces of classical modular forms, using the theory of overconvergent modular forms. The algorithms have a running time which grows linearly with the logarithm of the weight and are well suited to investigating the dimension variation of certain p-adically defined spaces of classical modular forms.

MSC classification

Secondary: 11G18: Arithmetic aspects of modular and Shimura varieties 11Y16: Algorithms; complexity 11-04: Explicit machine computation and programs (not the theory of computation or programming)
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 14 , 2011 , pp. 214 - 231
Copyright
Copyright © London Mathematical Society 2011

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