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A Simple Proof of the Modular Identity for Theta Functions
Proceedings of the American Mathematical Society
Vol. 131, No. 11 (Nov., 2003), pp. 3305-3307
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1194635
Page Count: 3
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The modular identity arises in the theory of theta functions in one complex variable. It states a relation between theta functions for parameters τ and -1/τ situated in the complex upper half-plane. A standard proof uses Poisson summation and hence builds on results from Fourier theory. This paper presents a simple proof using only a uniqueness property and the heat equation.
Proceedings of the American Mathematical Society © 2003 American Mathematical Society