On the $U_p$ operator acting on $p$-adic overconvergent modular forms when $X_0(p)$ has genus 1
| dc.creator | Kilford, L. J. P. | |
| dc.date | 2008-10-27 | |
| dc.date.accessioned | 2026-07-07T10:13:23Z | |
| dc.date.available | 2026-07-07T10:13:23Z | |
| dc.description | In this article we will show how to compute $U_p$ acting on spaces of overconvergent $p$-adic modular forms when $X_0(p)$ has genus 1. We first give a construction of Banach bases for spaces of overconvergent $p$-adic modular forms, and then give an algorithm to approximate both the characteristic power series of the $U_p$ operator and eigenvectors of finite slope for $U_p$, and present some explicit examples. We will also relate this to the conjectures of Clay on the slopes of overconvergent modular forms. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0810.4788 | |
| dc.identifier | http://arxiv.org/abs/0810.4788 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/172510 | |
| dc.subject | Number Theory | |
| dc.subject | 11F03 | |
| dc.title | On the $U_p$ operator acting on $p$-adic overconvergent modular forms when $X_0(p)$ has genus 1 | |
| dc.type | text |