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Computational Methods and Function Theory 6 (2006), No. 2, 447--458
Copyright Heldermann Verlag 2006

Angular Distribution of Zeros of the Partial Sums of ez via the Solution of Inverse Logarithmic Potential Problem

Vladimir V. Andrievskii
andriyev@math.kent.edu , Department of Mathematical Sciences, Kent State University, Kent, OH 44242, U.S.A.

Amos J. Carpenter
acarpent@butler.edu , Department of Mathematics and Actuarial Sciences, Butler University, Indianapolis, IN 46208, U.S.A.

Richard S. Varga
varga@math.kent.edu , Department of Mathematical Sciences, Kent State University, Kent, OH 44242, U.S.A.

[Abstract-pdf] [Abstract-ps]

We continue the work of Szegö [18] on describing the angular distribution of the zeros of the normalized partial sum sn(nz) of ez, where sn(z):=Σk=0nzk/k!. We imbed this problem in some inverse problem of potential theory and prove a so-called Erdös-Turán-type theorem, which is of interest in itself.

Keywords: Szegö curve, logarithmic potential, harmonic measure.

MSC 2000: Primary 30E10; Secondary 30C15, 31A15, 41A30.

[FullText-pdf (284 K)] [FullText-ps (476 K)]