3 problems

Let $F$ be a number field, let $G=GL_n$, and let $E$ be a coefficient field. Write $X^+_{00}(\operatorname{Res}_{F/\mathbb{Q}}(T_0)\times E)$ for the set of strongly-pure dominant…

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…

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