Timeline for Computing Thompson series for the monster group
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| Aug 25, 2013 at 15:34 | vote | accept | user43645 | ||
| Aug 25, 2013 at 4:53 | comment | added | Noam D. Elkies | The periodicity should follow from asymptotic formulas for the coefficients of these modular functions analogous to those given by Hardy and Ramanujan for the partition function. There are also various elementary approaches; the simplest example is a proof that the $X_0(2)$ Hauptmodul $$ \left(\frac{\eta(q)}{\eta(q^2)}\right)^{24} = q^{-1} - 24 + 276q - 2048q^2 + 11202q^3 - 49152q^4 + - \cdots $$ has alternating signs by rearranging the product $\eta(q)/\eta(q^2)$ as $(1-q)(1-q^3)(1-q^5)(1-q^7)\cdots$ which clearly becomes nonnegative on substituting $-q$ for $q$. | |
| Aug 24, 2013 at 14:34 | history | answered | Jeff Harvey | CC BY-SA 3.0 |