5 problems

Complete quasi-equidistribution conjecture. Let $\gamma$ be the largest root of the polynomial $x^2-px-q$ for $1\leq q\leq p$. The van der Corput sequence in base $\gamma$ is c.q.e…

Let $p_n=\mathfrak{F}_n$ be the $n$th Fibonacci number and let $\mu_n=\sigma_{p_{n-1},0}$. Define $z(1)=z(2)=z(3)=1$, $z(4)=2$, and, for subsequent indices,…

Let $\omega=\omega_b$ be the permutation obtained from Faure's algorithm. For $n\geq 4$, set $B_n=[2^{n-1},2^n-1]$, $b_n=2^n-1$, and…

Let $\widetilde{Y}_2$ be the symmetrized van der Corput sequence in base $2$, and let $L_{p,N}$ denote its $L_p$-discrepancy. Theorem-level results establish … for every…

Optimality conjecture. This value is best possible among all choices of $\Sigma$; equivalently,