7 problems

The inert quadratic order conjecture. For each $m\geq 1$,

Fix $d\geq4$, write $\Delta=(d+1)(d-3)=f^2\Delta_0$ with $\Delta_0$ a fundamental discriminant, and let $f'\mid f$. Let $\mathcal M$ satisfy the extended order-to-multiplet conject…

Fix $d\in\mathbb Z_{>0}$, $d\neq3$, write $\Delta=\Delta_d=(d+1)(d-3)=f^2\Delta_0$ with $\Delta_0$ a fundamental discriminant, and let $\mathcal M(f')$ be the multiplet indexed by…

Fix $d\in\mathbb Z_{>0}$, $d\neq3$, set $\Delta=\Delta_d=(d+1)(d-3)$ and $K=\Q(\sqrt{\Delta})$. Let $\mathcal O_\Delta$ and $\mathcal O_K$ denote the quadratic order of discriminan…

Fix $d\in\mathbb Z_{>0}$, $d\neq3$, let $\Delta=(d+1)(d-3)$, and let $\mathcal O_\Delta$ be the quadratic order of discriminant $\Delta$. Geometric Count Conjecture. The number of…

Fix a positive integer $d\neq 3$, let $\Delta_d=(d+1)(d-3)$, and write $\Delta_d=f^2\Delta_0$, where $\Delta_0=\operatorname{disc}(\mathcal O_{K_d})$ and $K_d=\Q(\sqrt{\Delta_d})$.…

Let $d_1$ and $d_2$ be discriminants of quadratic imaginary orders, and fix an integer $t$. Let … Assume that the conductors of $d_1$ and $d_2$, together with $m$, have no simultan…