The zeros of Faber polynomials for an \(m\)-cusped hypocycloid (Q1335035)

The location, density and asymptotic behavior of the zeros of Faber polynomials \(F_ n\) associated with the closed region bounded by the \(m\)-cusped hypocycloid with equation \(z= \exp (i\theta)+ 1/(m-1)\exp (- (m-1) i\theta)\) are determined. The main result says that for each \(n\geq 1\) all zeros of \(F_ n\) are located on the set \(S_ m= \{x\omega^ k\): \(0\leq x< m/(m-1)\), \(k=0,1, \dots, m-1\), \(m\geq 2\}\), where \(\omega= \exp (2\pi i/m)\).