On the cuspidality of pullbacks of Siegel Eisenstein series and applications to the Bloch-Kato conjecture

Jim Brown

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 ${\bar{\rho }}_f$ is irreducible. Under so…