Li-Jie Wang

Interlacing on the Unit Circle via Coefficientwise Reciprocals

Let $f(z)=\sum_{k=0}^{n}a_kz^k$ be a polynomial with positive coefficients, and define its coefficientwise reciprocal by $f^{\#}(z)=\sum_{k=0}^{n}\frac{z^k}{a_k}.$ It is known that if $f$ is palindromic and has only negative real zeros, then all zeros of $f^{\#}$ lie on the unit circle. We prove that if $p$ and $q$ are...