2 problems

Let $(f,g,h)$ have weights $(k,\ell,m)$ with $k\geq\ell+m$ and $k,\ell,m\geq2$, and let $M(f\otimes g\otimes h)$ be the associated triple-product motive. Put $c=(k+\ell+m-2)/2$ and…

Assume the local root numbers of $L(E,\rho_{gh},s)$ are $+1$, its order of vanishing at $s=1$ is $2$, and the stated hypotheses on $p$, the Hida families, and the classicality of…