Complex Zolotarev polynomials on the real interval [-1,1] (Q1801551)

Let \(\rho=\sigma+i\tau\) be a given complex number, then the polynomial \(z^ n+\rho z^{n-1}+a_{n-2}z^{n-2}+\cdots + a_ 0\) \((a_ j\in \mathbb{C}, j=0,\dots,n-2)\) with minimal Chebyshev norm on the intervall \([- 1,1]\) is called the \(n\)-th Zolotarev polynomial for \(\rho\). The authors characterize Zolotarev polynomials for the case of nonzero values of \(\sigma\) and \(\tau\) by extremal points and show some relationship with real Zolotarev polynomials.