5 problems

Non-isotropic $(2,2)$ meromorphicity conjecture. The image of $\frac{i^{m}}{2}\Phi_{L,m,m,0}$ under $\frac{1}{-4\pi^{2}}R_{m}^{(2)}$, namely…

$S_{m}^{(b_{-})}$ operator conjecture. For any dimension $b_{-}$ and any weight $m$, there exists an operator $S_{m}^{(b_{-})}$ satisfying properties (i)--(vii) stated in the sourc…

Modularity conjecture. The formal generating series is the $q$-expansion of a function

Vanishing conjecture. If $\xi(f)=0$, then

Let $F$ be a totally real number field, let $\boldsymbol{c}$ be an odd square-free level, let $g\in S_{\mathbf{2}}(\boldsymbol{c})$ be a newform, and let $v_g$ be a Hecke eigenvect…