5 problems

A continued fraction has partial numerators $a_n$ and partial denominators $b_n$, with the displayed initial terms determining the pattern. Continued fraction conjecture for…

Let $\mathbb{R}_{S_n}$ be the reals at definability level $S_n$, let $\mathbb{R}_{S_\omega}=\bigcup_{n\in\mathbb{N}}\mathbb{R}_{S_n}$, and let $\mathbb{A}_{S_n}$ and…

Let $X$ be a simply connected elliptic space, and let $\frak{pp}_{\mathbb R}(X;1)$ denote its real stabilization threshold. Let $P(s)=P_X^{\pi}(s)$ and $Q(s)=P_X(s)$. Transcendence…

The $\pi$–$e$ counting conjecture. As $x\to\infty$,

The multiplicative-independence counting conjecture. The numbers $\alpha$ and $\beta$ are multiplicatively independent if and only if