3 problems

Let $\Omega\subset\mathbb{R}^2$ be a convex domain containing the origin in its interior, and let … Assume that the boundary of $\Omega$ is smooth and has positive curvature everyw…

Let $F_Q$ be the set of all reduced fractions in $[0,1]$ with denominator at most $Q$. For a reduced fraction $p/q\in F_Q$, let $L(p/q,q)$ be the unsymmetrized lattice and let…

Let $L(\alpha,N)$ be the unsymmetrized lattice associated with $\alpha\in[0,1]$ and $N$, and let $D_2$ denote its $L^2$ discrepancy. Suppose that $\alpha$ is chosen randomly from…