6 problems

Hayman's conjecture. The differential polynomial $f^n f'$ cannot have any non-zero generalized Picard exceptional values.

Let $w^\alpha$ be the coordinates obtained from the Dubrovin–Zhang quasi-Miura transformation of the dispersionless hierarchy, and consider the transformed equations, Hamiltonians…

Boris Shapiro's second conjecture.

Let $p$ be a real polynomial of degree $n\geq 2$, and let $Z_\mathbb{C}(p)$ denote the number of its non-real zeros, counted with multiplicity. For a real rational function, let…

Generalized Yang's conjecture. If $f(z)^n f^{(k)}(z)$ is a periodic function, then $f(z)$ is also a periodic function.

Let $f$ be a real meromorphic function in the plane, with finitely many zeros and non-real poles, and not of the form … where $S$ is a rational function and $P$ is a polynomial. La…