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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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On Dirichlet Series, Fourier Series and Functional Equations
by
Eugenio P. Balanzario
UNAM-Morelia

We prove a functional equation for the Mellin transform of a periodic Fourier series. As a first application we obtain a new proof of the functional equation for the general periodic Dirichlet series. We also produce Dirichlet series, which like a famous example of Davenport and Heilbronn, satisfy functional equations and have zeros off the critical line.

Date received: January 13, 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 # cadx-16.