Slopes of modular forms and the ghost conjecture (unabridged version)
Number Theory
2016-11-09 v2
Abstract
We formulate a conjecture on slopes of overconvergent p-adic cuspforms of any p-adic weight in the Gamma_0(N)-regular case. This conjecture unifies a conjecture of Buzzard on classical slopes and more recent conjectures on slopes "at the boundary of weight space".
Cite
@article{arxiv.1607.04658,
title = {Slopes of modular forms and the ghost conjecture (unabridged version)},
author = {John Bergdall and Robert Pollack},
journal= {arXiv preprint arXiv:1607.04658},
year = {2016}
}
Comments
39 pages, 2 figures, 6 tables. Changes from v1: Removed Section 7 (put on arXiv separately at 1611.01497) and fixed a minor typo in Section 6. We do not plan to publish the paper with this length at this time. This manuscript will be perpetually available, so it is renamed the "unabridged version". A condensed version (absent the combinatorial proofs contained here) will soon be available