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A Simple Proof of the Modular Identity for Theta Functions

Wim Couwenberg
Proceedings of the American Mathematical Society
Vol. 131, No. 11 (Nov., 2003), pp. 3305-3307
Stable URL: http://www.jstor.org/stable/1194635
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Simple Proof of the Modular Identity for Theta Functions
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Abstract

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.

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