Upper bounds for constant slope p-adic families of modular forms
Author: John Bergdall
Source: Selecta Mathematica-New Series, 25 (4):10.1007/s00029-019-0505-8
Publication Type: Journal Article
Summary: We study p-adic families of eigenforms for which the p-th Hecke eigenvalue ap has constant p-adic valuation ("constant slope families"). We prove two separate upper bounds for the size of such families. The first is in terms of the logarithmic derivative of ap while the second depends only on the slope of the family. We also investigate the numerical relationship between our results and the former Gouvea-Mazur conjecture.