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
a2 Mathematical Institute, 24–29 St Giles', Oxford OX1 3LB, UK

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


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.