10 problems

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

Let $(G,H,\xi)$ be a Gross–Prasad triple attached to an admissible pair $(W,V)$ over $\mathbb{R}$. Let $m(\pi)=\dim \operatorname{Hom}_{H(\mathbb{R})}(\pi,\xi)$ for an irreducible…

Let $F$ be a totally real number field, let $r$ be a positive integer, and let $A$ be an elliptic curve over $F$ with no complex multiplication over $\ovl F$. Suppose there exist a…

Let $0boldsymbol{pi}$ be a cuspidal automorphic representation of $0operatorname{GSp}4$ and let $0boldsymbol{sigma}1, 0boldsymbol{sigma}2$ be cuspidal automorphic representation…

Let $(\Pi,\underline{\mathcal G})$ be a split pair with $\Pi_p$ ordinary, and let $\mathfrak X_\spadesuit$ be the classical specialisations in a region $\spadesuit$ whose archimede…

Global Gross–Prasad conjecture. The period is non-zero if and only if

Let $F$ be a number field, let $v$ be a place of $F$, let $\Pi_v$ be an irreducible smooth representation of $G(F_v)$, and let $\Sigma_v=\Sigma_{1,v}\boxtimes\Sigma_{2,v}$ be an ir…

Let $V_{m+1}$ be an orthogonal space of dimension $m+1$, and let $V_m$ be a non-degenerate codimension-one subspace. Assume that…

Let $V'$ and $U'$ be the quadratic spaces defining $SO(V')$ and $SO(U')$, and let $P_{V',U'}$ be the automorphic period. Let $\Pi\boxtimes \overline{\pi}$ be a tempered automorphic…

Let $F$ be a non-Archimedean local field and let $V=X+D+W+Y$ be a quadratic space over $F$, with $W$ a quadratic subspace of codimension $2k+1$. Let ${\rm Bes}(W;k)$ denote the rel…