4 problems

Local Ohno–Nakagawa box conjecture. The lattices $\mathcal V_{\tau,\tau^{n-1}f}$ and $\mathcal V_{2\tau^{-1},(2\tau^{-1})^{n-1}f}$ are naturally dual with duality constant…

Let $K$ be a local field with $\operatorname{char}K\neq2$, let $n$ be odd, and let $\tau$ be a nonzero parameter. Let $\mathcal V_{\tau,\tau^{n-1}f}$ and…

Let $K$ be a $2$-adic local field and let $0\leq t\leq s\leq e=v_K(2)$. Let $C_1\subseteq C_2$ be orders in a cubic $K$-algebra $R$ with $C_2/C_1\cong\mathcal{O}_K/\pi^{s-t}$ cycli…

Let $n$ be a positive odd integer. Let $f$ be a polynomial of degree $n$ with no multiple roots and only one real root. A $2\times n\times n$ box is a pair $(A,B)$ of $n\times n$ i…