Double roots of [-1, 1] power series and related matters

@article{Pinner1999DoubleRO,
  title={Double roots of [-1, 1] power series and related matters},
  author={Christopher Pinner},
  journal={Math. Comput.},
  year={1999},
  volume={68},
  pages={1149-1178}
}
Abstract. For a given collection of distinct arguments ~ θ = (θ1, . . . , θt), multiplicities ~k = (k1, . . . , kt), and a real interval I = [U, V ] containing zero, we are interested in determining the smallest r for which there is a power series f(x) = 1 + ∑∞ n=1 anx n with coefficients an in I, and roots α1 = re2πiθ1 , . . . , αt = re2πiθt of order k1, . . . , kt respectively. We denote this by r(~ θ,~k; I). We describe the usual form of the extremal series (we give a sufficient condition… CONTINUE READING