You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. 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
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
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.
Preview not available
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