Birkhoff interpolation on non-uniformly distributed roots of unity

This paper studies some cases of (0,m)-interpolation on non-uniformly distributed roots of unity that were not covered before. The interpolation problem uses as nodes the zeros of (z ^k +1)(z ³–1) with k=3n+1, 3n+2. Proof of the regularity is more intricate than when k is divisible by 3, the case included in a previous paper by the authors. The interpolation problem appears to be regular for mk+3, a result that is in tune with the case k=3n mentioned before. However, it is necessary to treat the full general 18×18 linear system. For small values of m the determinant is calculated explicitly using MAPLE V, Release 5.