A New Proof For The Transformation Laws of Theta Functions
Maher Me'meh, Ali Saraeb
TL;DR
This paper presents a novel proof for the transformation laws of the four Jacobi theta functions by leveraging Gordon's proof of the Dedekind eta function's transformation law, offering a new perspective on classical results.
Contribution
It introduces a new proof method for theta function transformations based on Gordon's approach, differing from traditional techniques.
Findings
Successfully derives the transformation laws of all four Jacobi theta functions.
Provides a new proof technique connecting eta function transformations to theta functions.
Enhances understanding of the relationship between eta and theta functions.
Abstract
We prove the transformation laws of the four Jacobi theta functions using Gordon's proof for the transformation law of the Dedekind eta function.
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Taxonomy
TopicsAdvanced Mathematical Identities · Molecular spectroscopy and chirality · Advanced Algebra and Geometry