"Upper bounds for constant slope p-adic families of modular forms" by John Bergdall
 

Document Type

Article

Version

Author's Final Manuscript

Publication Title

Selecta Mathematica

Volume

25

Publication Date

2019

Abstract

We study p-adic families of eigenforms for which the p-th Hecke eigenvalue 𝑎𝑝 a p 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 a p while the second depends only on the slope of the family. We also investigate the numerical relationship between our results and the former Gouvêa–Mazur conjecture.

DOI

http://doi.org/10.1007/s00029-019-0505-8

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 1
  • Usage
    • Downloads: 133
    • Abstract Views: 12
  • Captures
    • Readers: 1
see details

Included in

Mathematics Commons

Share

COinS