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- Title
MULTIPLE ROOTS OF [-1, 1] POWER SERIES.
- Authors
BEAUCOUP, FRANK; BORWEIN, PETER; BOYD, DAVID W.; PINNER, CHRISTOPHER
- Abstract
We are interested in how small a root of multiplicity k can be for a power series of the form f(z:= 1+∑n=1aizi with coefficients ai in [1, 1]. Let r(k) denote the size of the smallest root of multiplicity k possible for such a power series. We show thatformula hereWe describe the form that the extremal power series must take and develop an algorithm that lets us compute the optimal root (which proves to be an algebraic number). The computations, for kd27, suggest that the upper bound is close to optimal and that r(k)<1c/(k+1), where c=1.230&.
- Subjects
MULTIPLICITY (Mathematics); POWER series; MATHEMATICAL forms; MATHEMATICAL formulas; ALGORITHMS; ALGEBRAIC number theory
- Publication
Journal of the London Mathematical Society, 1998, Vol 57, Issue 1, p135
- ISSN
0024-6107
- Publication type
Article
- DOI
10.1112/S0024610798005857