4 problems

Let $x\in\mathbb{R}_{>1}$, and let $[x]_q$ be its q-analogue defined by the corresponding Laurent series. Set … Leclere's convergence-radius conjecture. For every…

Let $p$ be a positive integer, and let $a$ and $b$ be numerators of irreducible fractions with common denominator $p$, satisfying $ab\equiv -1\pmod p$. The denominators are denoted…

For a real number $x>0$, let $[x]_q$ denote the associated $q$-deformation and let $R(x)$ be the radius of convergence of its Taylor series. Write … for the golden ratio, and let…

Factorization conjecture. If $r$ is a multiple of $3$, then $\mathcal{R}(q)$ is a multiple of