Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T17:37:05.627Z Has data issue: false hasContentIssue false
  • English
  • Français

Slopes of overconvergent 2-adic modular forms

Published online by Cambridge University Press:  21 April 2005

Kevin Buzzard  and
Frank Calegari
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
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.

Keywords

p-adic modular formsslopes of modular forms11F1114G3511F80
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 3 , May 2005 , pp. 591 - 604
Copyright
Foundation Compositio Mathematica 2005