A Maple Rendition of George Polya's Elementary Proof of the Modularity of the Theta Function


Dr. Z.'s Experimental Mathematics Spring 2018 class

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Written: April 24, 2018

One day every matheamtics paper will be machince checkable, and even machine-derivable, but there are aleady quite a few cases where, modulo human trivial ramblings, the job of the readers can be made so much easier. The readers are welcome to copy-and-paste the Maple code in this paper and verify for themselves.

This short note was a group effort in Dr. Z.'s Experimental Mathematics Spring 2018 class. The students were: Yonah Biers-Ariel, Matthew P. Charnley, Amit Harel, George D. Hauser, Edna L. Jones, Ahsan Z. Khan, Brooke Logan, Yukun Yao, Anthony Zaleski. The instructor was Doron Zeilberger.

It is based on Richard Bellman's nice version from pp. 40-41 from his classic book "A Brief Introduction to Theta Functions" that we strongly recommend.

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

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