Timeline for Dedekind eta function identity involving two complex variables
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2012 at 16:14 | comment | added | Tito Piezas III | Thank you, Dr. Elkies. Hart was kind enough to reply to my query, and said that a more recent paper, homepages.warwick.ac.uk/~masfaw/newidentity.pdf (Example 1) showed it was a special case true for all odd prime p. | |
| Sep 11, 2012 at 17:16 | comment | added | Noam D. Elkies | The expansion of $\eta^3$ involves only terms $\pm n q^{n^2/8}$ with $n$ odd. The sum over $k$ seems to isolate terms with $n^2 + {n'}^2$ divisible by $p$, and if $p\equiv -1 \bmod 4$ then $p|n^2 + {n'}^2$ if and only if $p|n$ and $p|n'$, from which the identity should follow. | |
| Sep 11, 2012 at 15:49 | history | asked | Tito Piezas III | CC BY-SA 3.0 |