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Slopes of overconvergent 2-adic modular forms

Published online by Cambridge University Press:  21 April 2005

Kevin Buzzard
Affiliation:
Department of Mathematics, Imperial College, 180 Queen's Gate, London SW7 2AZ, UKbuzzard@ic.ac.uk
Frank Calegari
Affiliation:
Department of Mathematics, Harvard University, Science Center, 1 Oxford Street, Cambridge, USAfcale@math.harvard.edu
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Abstract

We explicitly compute all the slopes of the Hecke operator U2 acting on overconvergent 2-adic level 1 cusp forms of weight 0: the nth slope is 1 + 2v((3n)!/n!), where v denotes the 2-adic valuation. We formulate an explicit conjecture about what these slopes should be for weight k forms.

Type
Research Article
Copyright
Foundation Compositio Mathematica 2005

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