2 problems

Let $p$ and $q$ be holomorphic polynomials with $n:=\deg p$ and $m:=\deg q$, and suppose that $p$ is not a constant multiple of $q$. A logharmonic polynomial is a function of the f…

Let $N(n,m)$ denote the maximum valence of a harmonic polynomial $p(z)+\overline{q(z)}$, where $p$ and $q$ are complex polynomials of degrees $n>m>0$. Lundberg–Lerario–Lundberg con…