9 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…

Wirsing's conjecture. For all transcendental $\xi$, the degree $\omega^*$ can be made arbitrarily close to $n+1$.

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

Normality conjecture for $\pi$. The constant $\pi$, and other natural transcendental constants, should be normal in every base $b\geq 2$.

Let $e$ denote the base of the natural logarithm and let $\pi$ denote the ratio of a circle's circumference to its diameter. Lambert's conjecture. $e$ and $\pi$ are transcendental…

Let $\mathbb{P}$ denote the set of periods, namely complex numbers whose real and imaginary parts are values of absolutely convergent integrals of rational functions with rational…