6 problems

Nonsplit Bianchi quantum unique ergodicity conjecture. If $H\in C_b(\Gamma\backslash\mathbb{H})$ is fixed, then

Let $E$ be one of the CM elliptic curves $E=\mathbb{C}/\mathbb{Z}[i]$ or $E=\mathbb{C}/\mathbb{Z}[\rho]$, let $\mathfrak{p}$ be the relevant prime ideal, let $T_k$ be the coefficie…

Let $\Gamma_0({\mathfrak p})$ be a congruence subgroup inside a fixed Bianchi group, where ${\mathfrak p}$ is a prime ideal of residue degree one. Write $N{\mathfrak p}$ for its no…

Let $K$ be an imaginary quadratic field, let ${\mathcal O}_K$ be its ring of integers, and let $\Gamma_0({\mathfrak p})$ denote the corresponding congruence subgroup for a prime id…

Nonvanishing conjecture. This restricted differential is nonzero.

Long–Maclachlan–Reid conjectures. 1. There exist infinitely many pairs of prime ideals $\mathfrak{p}_1,\mathfrak{p}_2$ in $\mathbb Z[i]$ such that