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- Title
An Elementary Proof of the Transformation Formula for the Dedekind Eta Function.
- Authors
Kong, Z. Y.; Teo, L. P.
- Abstract
In this work, we give an elementary proof of the transformation formula for the Dedekind eta function under the action of the modular group PSL (2;Z). We start by giving a proof of the transformation formula η(τ) under the transformation τ →-1/τ, using the Jacobi triple product identity and the Poisson summation formula. After we establish some identities for the Dedekind sum, the transformation formula for η(τ) under the transformation induced by a general element of the modular group PSL (2;Z) is derived by induction.
- Subjects
MODULAR groups; DEDEKIND sums; HYPERGEOMETRIC series; FUNCTIONAL equations
- Publication
Armenian Journal of Mathematics, 2024, Vol 16, Issue 4, p1
- ISSN
1829-1163
- Publication type
Article
- DOI
10.52737/18291163-2024.16.4-1-22