10 problems

Meromorphic-power conjecture. Then there is an integer $N$ such that

Let $\mathfrak a_{\mathbb R}^{*,+}$ be the positive dual cone, let $\overline{\mathfrak a_{\mathbb R}^{*,+}}$ be its closure, and let…

Improved error-term conjecture. In all terms above, the error term $o(X)$ can be replaced by $O(X^{1/2+\varepsilon})$ for any $\varepsilon>0$, where the implied constant only depen…

Sarnak–Xue conjecture. The multiplicity of $\pi$ satisfies

Weighted Langlands–Shelstad transfer conjecture. For each $G$ and $M$, there is a function $\hat{S}^{{\tilde G}'}_{{\tilde M}'}(\delta',f')$ on … such that

Let $E \geq F' \geq F$ be a tower of number fields, let $S$ be a finite set of places of $F$ containing the infinite places, and let $S'$ and $S_0$ be the places of $F'$ and $E$ ab…

Let $F$ and $E$ be number fields as in the paper, let $n$ be a positive integer, and let $_{E/F}(\Sigma_{\phi}^{S_0}(X))$ denote the associated base-change test function. For a cus…

Let $\mathbf G$ be a connected reductive linear algebraic group over $\mathbb Q$, let $\eta:\mathbf G\to\operatorname{GL}(n)$ be a faithful rational representation, and let…

Absolute convergence conjecture. For every $f\in C_c^\infty(G(\mathbb A)^1)$, one has

The weak orthogonality relation. For positive integers $m_1,\ldots,m_{N-1}$,