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# 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} }

- Published 1999 in Math. Comput.
DOI:10.1090/S0025-5718-99-01042-X

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