5 problems

Let $G$ be the reductive group considered in the paper, let $\Gamma\subset G(\mathbb{Q})$ be a congruence subgroup, and let $\Pi(K_\infty)$ denote the set of $K_\infty$-types. For…

Let $M:=M_1\times\ldots\times M_n$ be the product of at least two compact Riemannian manifolds without boundary, and let $d$ be its dimension. Denote by $N_M(\lambda)$ the eigenval…

Weyl law improvement conjecture. There exists $\delta>0$ such that

Weyl–Schanuel law. As $Q\rightarrow\infty$,

Let $X=\operatorname{SL}(2,\mathbb{Z})\backslash\mathcal{H}$ be the modular surface, and let $S(t)$ denote the Weyl remainder for its Maass spectrum. Square-root upper-bound conjec…