7 problems

The algebraicity–diagonal–global-boundedness conjecture. The following statements are equivalent:

Christol's conjecture. Every D-finite globally bounded function is the diagonal of a rational function.

Let $fin \mathbb{Q}[[z]]$ be a globally bounded and D-finite power series, and let $L^{\mathrm{min}}_f$ denote its minimal annihilating differential operator. Christol–André conjec…

Let $A(t)=\sum_{n\ge 0} a_n t^n\in\mathbb Z[[t]]$, suppose that $|a_n|<c^n$ for all $n\in\mathbb N$ and some $c>0$, and suppose that $A$ is D-finite. Christol's conjecture. Then…

Diagonal conjecture. If the generating series of a primary pseudo-polynomial is the diagonal of a rational fraction, then $(a_n)_{n\geq 0}$ is a polynomial.

Diagonal-positivity conjecture. The series $\operatorname{diag}_F$ is nonnegative if and only if

A rank $n$-diagonal is a diagonal satisfying the rank-$n$ condition described in the surrounding theory. Diagonal-rank separation conjecture. For every natural number $n$ there is…