Zeros of sections of exponential sums

Robert G. Mallison, Purdue University

Abstract

We derive the large n asymptotics of zeros of sections of a generic exponential sum. We divide all the zeros of the n-th section of the exponential sum into “genuine zeros”, which approach, as n → ∞, the zeros of the exponential sum, and “spurious zeros”, which go to infinity as n → ∞. We show that the spurious zeros, after scaling down by the factor of n, approach a “rosette”, a finite collection of curves on the complex plane, resembling the rosette. We derive also the large n asymptotics of the “transitional zeros”, the intermediate zeros between genuine and spurious ones. Our results give an extension to the classical results of Szego&huml; about the large n asymptotics of zeros of sections of the exponential, sine, and cosine functions.

Degree

Ph.D.

Advisors

Bleher, Purdue University.

Subject Area

Mathematics

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