# On a problem posed by P. Turán: Problem LXVI

by Kenier Castillo (Universidade de Coimbra)

The following problem appears in the posthumous paper of P. Turán, "On some open problems in Approximation Theory": "It is known that the zeros of the nth orthogonal polynomial (with respect to a Lebesgue-integral function on an interval) separate the zeros of the (n + 1)th polynomial. What corresponds to this fact on the unit circle?" The purpose of this talk is to extend in a simple and unified way the known results on Problem LXVI. It is a joint work with J. Petronilho. The talk is based on the work [1].

References:

[1] K. Castillo and J. Petronilho, "Refined interlacing properties for zeros of paraorthogonal polynomials on the unit circle", Proc. Amer. Math. Soc. (DOI: https://doi.org/10.1090/proc/14011).