11 problems

Let $F$ be the underlying local field, let $G_m=GL_m(F)$, and let $N$ and $\psi$ be the subgroup and character defining the twisted Jacquet module. Let $\pi$ be an irreducible smoo…

Let $G$ be a reductive $p$-adic group and let $\phi$ be a Langlands parameter, with associated L-packet $\Pi_\phi(G)$. A representation is generic if it admits a Whittaker model. G…

Let $bbG$ be a connected reductive group over $bbF$, let $bbphi$ be an $bbSL_2$-parameter, and let $L(s,bboperatorname{Ad}\circbbphi)$ denote its adjoint $L$-factor. Gross–Prasad–R…

Let $(G,H)$ be a strongly tempered spherical pair that is the Whittaker induction of $(G_0,H_0,\xi)$, with $G$ admitting a quasi-split pure inner form $G_{qs}$. Assume that…

Gross-Prasad--Rallis conjecture. The parameter $\phi$ is generic if and only if

Let $k$ be positive and even, let $f \in S_{2k-2(n+r)}(\operatorname{SL}_2(\mathbb{Z}))$ be a normalized Hecke eigenform, let $F^{(2n+2r)}$ be its Ikeda lift, and let…

Let $k$ be such that the indicated spaces are defined, and let $f \in S_{2k-4}(\operatorname{SL}_2(\mathbb{Z}))$ and $g \in S_k(\operatorname{SL}_2(\mathbb{Z}))$ be normalized Heck…

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

Refined Böcherer conjecture. For every such $K$ and $\Lambda$,

Böcherer's conjecture. There exists a constant $c_f$ depending only on $f$ such that, for every such $K$,

Let $f$ be a $p$-new eigenform, let $\mathfrak{p}$ be a prime above $p$, let $V_{\mathfrak{p}}(f)$ be the corresponding $p$-adic representation, let ${\Greekmath 011F}$ be a charac…