7 problems

Shapiro's conjecture. If two exponential sums in ${\cal E}$ have infinitely many zeros in common, they are both multiples of some third entire transcendental exponential sum in…

Ritt-type factorization conjecture. For every non-zero $E$-function $f$, there exist a unit $u\in\mathcal E^\times$, simple normalized $E$-functions $s_1,\ldots,s_p$ with pairwise…

Simple-factor obstruction conjecture. The failure of factoriality in $\mathcal E$ occurs only with simple functions.

The equality conjecture. For all $\ell,n\in{\mathbb N}$, we have

Generalized Shapiro's conjecture. If $f$ and $g$ are not multiples of the same transcendental exponential polynomial of order $q$, then

Weak irreducibility conjecture. Assuming Schanuel's conjecture, either ${\rm Zer}(f)$ is irreducible or every $m$-dimensional irreducible component of ${\rm Zer}(f)$ is contained i…

Fix $\a_1,\ldots,\a_n\in K^*$ such that no ratio $\a_i/\a_j$ is a root of unity, and consider the determinant equation … with $y_2,\ldots,y_n\in{\mathbb Z}$. Schlickewei–Viola conj…