(0,m) Pál-type interpolation on the Möbius transform of roots of unity

摘要

Define for integer m⩾1 and α a complex number with α2,αm≠1, the polynomial of degree mwm(α;z)=(z+α)m-(1+αz)m,whose (simple) zeros can be seen as the Möbius transforms of the mth roots of unity.In this paper it will be shown that (0,m) Pál-type interpolation on the zeros of {wn+m(α;z),wn(α;z)} is regular for all integers n,m⩾1 and complex numbers α with α2,αm,αn,αn+m≠1.