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Entire functions with zeros on a line
by
David Cardon
Brigham Young University
In 1926 Polya studied a method of obtaining entire functions all of whose zeros are on a given line. His application was to better understand the zeros of the Riemann zeta function. I will explain a generalization of his technique. In particular, let G be an entire function of order < 2 that is real on the real axis and has only real zeros. Then I construct certain distributions F such that the convolution integral \int-\infty\infty G(z-is) dF(s) is also an entire function with only real zeros.
Date received: March 17, 2000
Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caew-30.