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Computing overconvergent forms for small primes

Part of: Computational number theory Number theory Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 April 2015

Jan Vonk
Jan Vonk*
Affiliation:
Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG, United Kingdom email vonk@maths.ox.ac.uk

Abstract

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We construct explicit bases for spaces of overconvergent $p$-adic modular forms when $p=2,3$ and study their interaction with the Atkin operator. This results in an extension of Lauder’s algorithms for overconvergent modular forms. We illustrate these algorithms with computations of slope sequences of some $2$-adic eigencurves and the construction of Chow–Heegner points on elliptic curves via special values of Rankin triple product L-functions.

MSC classification

Primary: 11F03: Modular and automorphic functions 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 18 , Issue 1 , 2015 , pp. 250 - 257
Copyright
© The Author 2015 

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