3 papers
math.NT2023
Bounding Lifts of Markoff Triples mod
Elisa Bellah, Siran Chen, Elena Fuchs +1
In 2016, Bourgain, Gamburd, and Sarnak proved that Strong Approximation holds for the Markoff surface in most cases. That is, the modulo solutions to the equation $X_1^2+X_2^2+…
math.NT2020
A modular proof of the properness of the Coleman-Mazur eigencurve
Lynnelle Ye
We give a new proof of the properness of the Coleman-Mazur eigencurve. The question of whether the eigencurve satisfies the valuative criterion for properness was first asked by Co…
math.NT2020
Slopes in eigenvarieties for definite unitary groups
Lynnelle Ye
We generalize bounds of Liu-Wan-Xiao for slopes in eigencurves for definite unitary groups of rank to slopes in eigenvarieties for definite unitary groups of any rank. We show…