4 problems

Lewin–Vitek's conjecture. The interval

Let $k\in\mathbb{N}$ and define … Let $F_k(n)$ and $B_k(n)$ be the bounds defined in the paper. Eventual coincidence conjecture. If $2\leq k\leq 6$, then for every $n>k^2$, … If…

Let $n$ and $k$ be integers satisfying $2\leq k\leq n$. Let $B_h(n)$ and $\tilde U^k_h(n)$ be the functions introduced in the paper, and define … Here $rt_k(n)$ denotes the maximum…

Let $w_n=(n-1)^2+1$, and let $[a,b]^o$ denote the set of integers $k$ with $a\leq k\leq b$. A gap in the exponent set of primitive matrices of order $n$ is a set of consecutive int…