9 problems

Böcherer's conjecture. For every imaginary quadratic field $E$,

Liu's refined global Gross–Prasad conjecture. One has

Global Gan–Gross–Prasad conjecture. There exists a unique pair $(\pi_0,\sigma_0)$ in $\widetilde{\Pi}_{\phi_G\times\phi_H}[G_n^*\times H_m^*]$ such that

Let $d<0$ be a fundamental discriminant, let $K=\mathbb{Q}(\sqrt d)$, let $\operatorname{Cl}_K$ be the ideal class group of $K$, and let $w(K)\in\{2,4,6\}$ be the number of roots o…

Gan–Gross–Prasad inequality. If $\sigma$ shares a global Vogan packet with $\sigma_0$ but is not equivalent to $\sigma_0$, then

Generic Summand Conjecture. There exists a cuspidal realization ${\mathcal {C}}_\pi$ with first occurrence index $\ell_0$ and a suitable $k$-rational orbit…

Bessel-period obstruction conjecture. The integer $\ell$, with $0\leq\ell\leq {\mathfrak {r}}_n$, is not the first occurrence index of $\pi$.

Special case of global Gan–Gross–Prasad. If there is an automorphic form $\phi$ in the space of $\pi$ such that $B(\phi,\Lambda)\neq0$, then

Let $F$ be a number field, let $\mathbb A$ be its ring of adeles, and let $\Pi\boxtimes\Pi^\prime$ be an irreducible cuspidal representation of…