On the cuspidality of pullbacks of Siegel Eisenstein series and applications to the Bloch-Kato conjecture
| dc.creator | Brown, Jim | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:49:05Z | |
| dc.date.available | 2026-07-07T08:49:05Z | |
| dc.description | Let $k > 3$ be an integer and $p$ a prime with $p > 2k-2$. Let $f$ be a newform of weight $2k-2$ and level 1 so that $f$ is ordinary at $p$ and $\barρ_{f}$ is irreducible. Under some additional hypotheses we prove that $ord_{p}(L_{alg}(k,f)) \leq ord_{p}(# S)$ where $S$ is the Pontryagin dual of the Selmer group associated to $ρ_{f} \otimes ε^{1-k}$ with $ε$ the $p$-adic cyclotomic character. We accomplish this by first constructing a congruence between the Saito-Kurokawa lift of $f$ and a non-CAP Siegel cusp form. Once this congruence is established, we use Galois representations to obtain the lower bound on the Selmer group. | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/0712.2227 | |
| dc.identifier | http://arxiv.org/abs/0712.2227 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144172 | |
| dc.subject | Number Theory | |
| dc.subject | 11F33, 11F67, 11F46, 11F80 | |
| dc.title | On the cuspidality of pullbacks of Siegel Eisenstein series and applications to the Bloch-Kato conjecture | |
| dc.type | text |