2 problems

Let $d$ be general, and choose integer points with coordinates satisfying $0\leq v_i<n_i$ for each $i$. Let the associated fractional parts be ordered and let $D$ denote the number…

For any real number $\theta$, write $\{\theta\}$ for its fractional part. Let $d=1$, let $w_1$ be any real frequency, and form the ordered fractional parts arising from the relevan…