6 problems

Let $H$ be a higher-rank semisimple group of the form … where each $F_i$ is a local field, each $\mathbf{G}_i$ is an absolutely almost simple $F_i$-group, and … For a group…

Let $k$ be a global field, let $S$ be a finite set of places, and let $\Gamma=G(\mathcal{O}_S)$. Write $r_n(\Gamma)$ for the number of irreducible representations of degree $n$, an…

Let … where each $K_i$ is a local field, each $G_i$ is an absolutely almost simple $K_i$-group, and … Let $\rho(\Gamma)$ denote the abscissa of convergence of the representation ze…

Representation-growth conjecture. (a) There exists a $2A$-periodic sequence $c_{q,1},c_{q,2},\ldots$ of positive numbers such that

Let $C>0$ be a constant. For each $n$ and prime $p$, consider the irreducible smooth representations of $SL_n(\mathbb{Z}_p)$, with dimension measured as the vector-space dimension…

Let … where each $K_i$ is a local field, each $G_i$ is an absolutely almost simple $K_i$-group, and … For a finitely generated group $\Gamma$, let $r_n(\Gamma)$ be the number of ir…