3 problems

Irrationality-exponent conjecture. The irrationality exponent of the first odd zeta constant satisfies

Badziahin's conjecture. Then $\mu(g_{\mathbf a}(b))=2$ for every $\mathbf a\in\mathbb Z^2$, except in the following three families:

Let $\xi$ be an irrational real number whose base-$b$ expansion is an automatic or morphic sequence for some integer $b\geq 2$. Bugeaud–Krieger–Shallit conjecture. The irrationalit…