4 problems

Sturmfels–Zworski conjecture. For generic reciprocal polynomials $P$ of even degree $d$, the first $d/2+1$ cyclic resultants determine $P$; for generic non-reciprocal polynomials,…

Let $K$ be the coefficient field, and let $f(x)\in K[x]$ be a generic monic polynomial of degree $d$. Its cyclic resultants are the associated sequence of resultants. Generic cycli…

Let $K$ be the coefficient field, and let $f(x)\in K[x]$ be a reciprocal monic polynomial of even degree $d$, meaning that $f(1/x)=x^d f(x)$. Its cyclic resultants are the associat…

Sturmfels–Zworski conjecture. A generic monic polynomial $f(x)\in\mathbb C[x]$ of degree $d$ is determined by its first $d+1$ cyclic resultants. Moreover, if $f$ is non-monic recip…