14 citations · 16 across the 3 of their papers we have counts for
3 papers
math.NT2005★ 14 cited
The 2-adic Eigencurve is Proper
Kevin Buzzard, Frank Calegari
For p=2 and tame level N=1 we prove that the map from the (Coleman-Mazur) Eigencurve to weight space satisfies the valuative criterion of properness. More informally, we show that…
math.NT2003★ 2 cited
Slopes of overconvergent 2-adic modular forms
Kevin Buzzard, Frank Calegari
The slope of a p-adic overconvergent eigenform of weight k is the p-adic valuation of its U_p eigenvalue. We find the slope of all 2-adic finite slope overconvergent eigenforms of…
math.NT2003
A counterexample to the Gouvea--Mazur conjecture
Kevin Buzzard, Frank Calegari
Gouvea and Mazur made a precise conjecture about slopes of modular forms. Weaker versions of this conjecture were established by Coleman and Wan. In this note, we exhibit explicit…