On the zeros of exponential polynomials

Abstract

with constant a's and with constant a's distinct from one another. The distribution of the zeros of such functions, and of more general functions in which the a's are polynomials in z, rather than constants, has been investigated by Tamarkin, Polya and Schwenglert. The very elegant results secured by them will be described, to some extent, below. The present writer has treated the question of factorizing an exponential polynomial into a product of exponential polynomials:. We present here two results. In ?1, we prove that if every zero of one exponential polynomial is also a zero of a second exponential polynomial, the quotient of the second function by the first is an exponential polynomial. In ?2, we study the function