Upper bounds for constant slope p-adic families of modular forms

Bergdall, John

doi:10.1007/s00029-019-0505-8

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Upper bounds for constant slope p-adic families of modular forms

MPS-Authors

/persons/resource/persons240743

Bergdall, John
Max Planck Institute for Mathematics, Max Planck Society;

External Resource

https://doi.org/10.1007/s00029-019-0505-8
(Publisher version)

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

arXiv:1708.03663.pdf
(Preprint), 348KB

Supplementary Material (public)

There is no public supplementary material available

Citation

Bergdall, J. (2019). Upper bounds for constant slope p-adic families of modular forms. Selecta Mathematica, 25(4): 59. doi:10.1007/s00029-019-0505-8.

Cite as: https://hdl.handle.net/21.11116/0000-0005-4334-5

Abstract

We study $p$-adic families of eigenforms for which the $p$-th Hecke eigenvalue $a_p$ 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 $a_p$ while the second depends only on the slope of the family. We also investigate the numerical relationship
between our results and the former Gouv\^ea--Mazur conjecture.