4 problems

Let $s_2(n)$ denote the number of ones in the binary expansion of $n$, and for each integer $t\ge 1$ define $c_t$ to be the natural density…

Asymptotic conjecture for $(2,k,k)$-numbers. For each $k$,

Heuristic exponent conjecture for $(2,1,2)$-numbers.

Let $s\in\mathbb{N}$ and let $\mathcal{S}$ be a sequence in $[0,1)^s$. Write $D_N^{\ast}(\mathcal{S})$ for its star discrepancy at $N$ points. Grand discrepancy conjecture. For eve…