Sequences of polynomials whose zeros lie on fixed lemniscates (Q1203470)

For a fixed integer \(k\geq 2\) the author studies sequences \(P_ n(z)\) with the following properties: (i) \(\deg P_ n\to\infty\); (ii) the zeros of all the \(P_ n\)'s on a certain lemniscate with \(k_ 1\leq k\) foci, one of which is the origin; (iii) the \(P_ n(z)\) can be cut in such a way that the zeros of the ``lower part'' all lie on the unit circle and those of the ``upper part'' lie on a lemniscate having the foci in (ii) excluding the origin.