Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T02:01:28.876Z Has data issue: false hasContentIssue false

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, [email protected]
Frank Calegari
Affiliation:
Department of Mathematics, Harvard University, Science Center, 1 Oxford Street, Cambridge, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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