3 problems

Minimum-support conjecture. The minimum number of nonzero coefficients needed for a polyanalytic polynomial of degree $n$ to have the maximum number of $n^2$ zeros is $n$.

Let $X$ be an arbitrary compact subset of the complex plane, and let $f$ be continuous on $X$ and bianalytic on the interior of $X$. A bianalytic rational function has the form … w…

Let $Q$ be the confining weight defining the polyanalytic Ginibre ensemble, and let the spectral droplet denote the limiting support of its eigenvalue distribution. The analytic ca…