6 problems

Let $cmathbf H$ be the torus defining the periods under discussion, let $clambda_j$ denote the relevant Laplacian eigenvalues, and suppose the period bound in Theorem has a power o…

Let $\phi\in\mathcal{S}_N^\mathrm{new}(\mathcal{O})$ be a normalized Hecke eigenform, let $\pi$ be the cuspidal representation generated by $\phi$, and let $Y(D;\pi)$ be the associ…

Symmetry conjecture. For $x>0$ and sufficiently small $\delta>0$,

Let $\pi=\otimes_v\pi_v$ be an irreducible cuspidal automorphic representation generated by the fixed Hecke eigenform, and let $\{\mathcal{E}_v\}_{v\in S_\mathcal{O}}$ be local qua…

Let $D$ be a quaternion algebra over $\mathbb{Q}$, let $G$ be the associated algebraic group, and let $S_\mathcal{O}$ be the relevant finite set of places. Let $\pi$ be an irreduci…

Let $\mathbf{B}_1$ and $\mathbf{B}_2$ be two non-isomorphic quaternion algebras over $F$, set $\mathbf{G}_j=\mathbf{PB}_j^\times$ for $j=1,2$, and let…