4 problems

Larcher–Stockinger conjecture. If for almost all $\alpha$ the pair correlations of $(a_n\alpha)_{n \in \mathbb{N}} \mod 1$ are not Poissonian, then the pair correlations of this se…

Almost-everywhere obstruction conjecture. If for almost all $\alpha$ the pair correlations of $((\lbrace a_n\alpha\rbrace)_{n\in\mathbb N})$ are not Poissonian, then the pair corre…

Let $(a(n))_{n\geq1}$ be a strictly increasing sequence of positive integers. Call it quasi-arithmetic if it has the finite-dimensional arithmetic-progression structure defined in…

Let $(a(n))_{n\geq1}$ be the sequence of integers used to form $A_N=\{a(1),\ldots,a(N)\}$, and let $E(A_N)$ denote its additive energy. For a real number $\alpha$, consider the seq…