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Dedekind Eta Function Product Identities by Michael SomosOver 6200 Dedekind Eta Function Product Identities collected by Michael Somos
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Over 6200 Dedekind Eta Function Product Identities collected by Michael Somos
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Dedekind Eta Function Product Identities by Michael Somos | eta.math.georgetown.edu Reviews
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Over 6200 Dedekind Eta Function Product Identities collected by Michael Somos
eta.math.georgetown.edu
A Remarkable eta-product Identity
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A Remarkable eta-product Identity. Michael Somos 23 Mar 2010. Early in 2005 I discovered a remarkable eta-product identity that was known most probably to a very few people implicitly and even fewer explicitly. In order to state the identity we first define the infinite product. 1 is required for convergence. This is the Dedekind eta function defined in terms of q. For brevity let e. For example, e. And so on. The following level 60 three term identity holds. Given a finite set S. If we allow non disjoin...
Commonly used functions in modular equations
http://eta.math.georgetown.edu/common.html
Commonly used functions in modular equations. Last updated 27 Feb 2016. This page has URL http:/ eta.math.georgetown.edu/common.html. Back to eta function product identities.
Dedekind Eta Function Product Identities of prime squared level
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A small collection of identities for the Dedekind Eta Function. I conjecture that for all prime p there is a unique identity for p 2 level. I have found the unique identity for some small primes in the following list. They are encoded in a condensed format for convenience for use with PARI/GP. Note that p 5 are not here but in the main level list since they have so few terms. P = 5: x25 6 30. P = 7: x49 8 56. P = 11: x121 60 660. P = 13: x169 14 182. P = 17: x289 72 1224. P = 19: x361 60 1140.
Explanation of using the table of identities
http://eta.math.georgetown.edu/explain.html
Explanation of using the table of identities. Suppose you have an identity involving functions that can be expressed in terms of Ramanujan's theta function f(-q) (the page Commonly used functions in modular equations. Has a list of these with definitions of each in terms of f(-q) . For example, consider the identity. A 3(q) = b 3(q) c 3(q) where a(), b(), c() are cubic AGM theta functions. Using the definitions given there you can rewrite the identity as. F 3(-q) 9 q f 3(-q 9) /f(-q 3) ) 3 =. Naika and D...
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Dedekind Eta Function Product Identities by Michael Somos
A collection of over 6200 identities for the Dedekind Eta Function. Nota bene: 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. A sample: the unique eta function product identity of level 9. All eta function product identities by prime squared level. One file per prime (all internal links). All eta function product identities by level.
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