Dedekind Eta Function Product Identities by Michael Somos

The Dedekind eta function satisfies many identities and many modular equations are equivalent to Dedekind eta product identities. Beginning in 2004 I started to collect those identities that I found and I put them in a canonical form that was inspired by Michael Trott's results from 2000. Some of them are equivalent to identities already in the literature and a reference is given if known to me. Some of the identities were found by Ramanujan. Many others are equivalent to identities that I found in my own research activities. This list of identities can be explored to formulate conjectures such as my conjecture about a unique and remarkable eta product identity. I have automated scripts to check all the identities in my collection but I offer no proofs of their correctness. Please don't publicize any internal links such as the level files and eta07.gp. Please inform me of any errors. Caveat emptor et caveat lector.

Brief explanation of using the table of identities.
Definitions for commonly used functions in modular equations.
A sample, the unique eta function product identity of level 4.
All eta function product identities by level - one file per level (internal link).
All 5948 identities (eta07.gp) (954kB, 17 May 2013) in one file (internal link).

Last updated 17 May 2013
This page has URL http://eta.math.georgetown.edu/index.html
My contact info: somos@cis.csuohio.edu.