Arithmetic properties of Fredholm series for p-adic modular forms
Number Theory
2017-02-28 v2
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 U_p 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.
Cite
@article{arxiv.1506.05307,
title = {Arithmetic properties of Fredholm series for p-adic modular forms},
author = {John Bergdall and Robert Pollack},
journal= {arXiv preprint arXiv:1506.05307},
year = {2017}
}
Comments
Final version. Numbering in main body different different from previous version. To appear in Proc. Lon. Math. Soc. 25 pages, 7 tables