2 problems

Let $L$ be a sublattice of $\mathbb{Z}^t$, let $N$ be large, let $K\subseteq[-N,N]^t$ be convex with volume $\gg N^t$, and let $a\in\mathbb{Z}^t$ have size $O(N)$. Assume that all…

Let $L$ be an affine sublattice of $\mathbb{Z}^t$. For each prime $p$, let $\alpha_p(L)$ be the local factor defined from the image $L_p$ of $L$ in $\mathbb{Z}_p^t$; a local obstru…