Document Type
Article
Version
Author's Final Manuscript
Publication Title
Proceedings of the London Mathematical Society
Volume
113
Publication Date
2016
Abstract
We study the relationship between recent conjectures on slopes of overconvergent p ‐adic modular forms ‘near the boundary’ of p ‐adic weight space. We also prove in tame level 1 that the coefficients of the Fredholm series of the Up operator never vanish modulo p , a phenomenon that fails at higher level. In higher level, we do check that infinitely many coefficients are non‐zero modulo p using a modular interpretation of the mod p reduction of the Fredholm series recently discovered by Andreatta, Iovita and Pilloni.
Citation
Bergdall, John and Robert Pollack. 2016. "Arithmetic properties of Fredholm series for p-adic modular forms." Proceedings of the London Mathematical Society, 113.3: 419-444.
DOI
http://doi.org/10.1112/plms/pdw031