5 problems

Rational-function series conjecture. This number is either rational or transcendental, and it is never a Liouville number. Moreover, if it is rational, then the series is telescopi…

Let $n\ge 2$ and let $I\subseteq\mathbb{R}$ be an open interval containing $0$. Let $\mathscr{L}_{n,n}$ denote the set of Liouville matrices, and let $\textswab{f}_k$ and…

Let $\theta$ be the fixed point of $x\mapsto \xi^x$ and define the iterated power towers by $h_1(\xi)=\xi$ and $h_{k+1}(\xi)=\xi^{h_k(\xi)}$ for $k\geq 1$. An ultra-Liouville numbe…

Algebraic multiplier conjecture. For any $m>1$, there exists an algebraic number $\alpha$ of degree $m$ such that

Let $I$ and $f_{a,b}$ be as in Theorem. Let $A\subseteq\mathbb{Q}\setminus\{0\}$ satisfy $1\in A$ and the property that every non-zero integral multiple of each element of $A$ also…