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Computational Methods and Function Theory 5 (2005), No. 1, 143--151
Copyright Heldermann Verlag 2005

Bohr's Radius for Polynomials in One Complex Variable

Zdenka Guadarrama
zkali@uark.edu , Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701, U.S.A.

[Abstract-pdf] [Abstract-ps]

We consider complex polynomials of degree n that are bounded by one in the unit disc and give estimates on the size of the radius Rn of the disc where the sum of the moduli of the individual terms of the polynomial is less than one. We find that there are positive constants C_1, C_2 such that
C_1\frac{1}{3^{n/2}}< R_n-\frac{1}{3}< C_2\frac{\log n}{n}.
This result generalizes the celebrated theorem of Harald Bohr to polynomials of degree n.

Keywords: Bohr's Theorem.

MSC 2000: 41A25.

[FullText-pdf (228 K)] [FullText-ps (385 K)]