Compositio Mathematica



The 2-adic eigencurve at the boundary of weight space


Kevin Buzzard a1 and L. J. P. Kilford a2
a1 Department of Mathematics, Imperial College, South Kensington, London SW7 2AZ, UK buzzard@imperial.co.uk
a2 Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK l.kilford@gmail.com

Article author query
buzzard k   [Google Scholar] 
kilford ljp   [Google Scholar] 
 

Abstract

We prove that, near the boundary of weight space, the 2-adic eigencurve of tame level 1 can be written as an infinite disjoint union of ‘evenly spaced’ annuli, and on each annulus the slopes of the corresponding overconvergent eigenforms tend to zero.

(Received February 4 2004)
(Accepted May 26 2004)
(Published Online April 21 2005)


Key Words: eigencurve; slopes of modular forms; overconvergent modular forms.

Maths Classification

11F33; 14G22.