5 problems

Let $F$ be a Hecke–Maass cusp form for $\operatorname{SL}_{N}(\mathbb{Z})$, and let … be its Satake parameter at a prime $p$, where $\mathsf{T}_0$ is the standard maximal torus of…

Let $f_d$ be a quadratic twist and let $\alpha_{f_d}(p)$ and $\beta_{f_d}(p)$ be its Satake parameters at a prime $p$. Ramanujan–Petersson conjecture. The conjecture states that ……

Let $k$ be a number field, let $\mathrm{G}$ be a connected reductive group over $k$, and let $\pi=\bigotimes_v\pi_v$ be an automorphic representation of $\mathrm{G}(\mathbb{A}_k)$…

Let $p$ be a finite prime and let $\pi\in\hat{\mathbb{X}}_{\mathrm{gen}}$ be a generic irreducible unitary standard automorphic representation. Write its Langlands parameters at…

Let $W'_F:= W_F \rtimes \mathbb C$ be the Weil–Deligne group. For a representation $\pi \in \Pi(G/F,J)$ with local Langlands parameter $\varphi_\pi: W'_F \rightarrow {}^LG$, let…