All Questions

Let $\Lambda$ be a lattice of $\mathbb{R}^n$, and $\lambda_i$ be the radius of the smallest ball containing $i$ linearly independent lattice vectors. The Minkowski successive minima inequality says ...

I am wondering if it is possible to produce an upper and/or lower bound on the number of integer lattice points that lie inside an $n$-dimensional ellipse. That is, given an $n$-dimensional ellipsoid ...

Let $L$ be a (full rank) lattice in $\mathbb{R}^t$ and let $K$ be a convex body. Minkowski's second theorem states that $$ \frac{2^t}{t!} \det(L) \leq \lambda_1 \cdot \ldots \cdot \lambda_t \text{Vol}(...

Given convex polytope $\mathcal P\subseteq\Bbb R^n$ with $\mathcal P_\Bbb Z\leq2^n$ integer points and given locations of $O(\log \mathcal P_\Bbb Z)$ integer points in some positions can we obtain $\...