Timeline for Deciding whether a given power series is modular or not
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2011 at 13:22 | history | bounty ended | Wadim Zudilin | ||
| Jan 2, 2011 at 13:19 | history | bounty started | Wadim Zudilin | ||
| Jan 1, 2011 at 13:52 | comment | added | Wadim Zudilin | @Kevin, thanks for this hint. Because I have no guess about the index of the underlying group in $\Gamma(1)$, I am not sure that $O(q^{1000})$ would be enough. I didn't try to expand so far (the coefficients grow extremely fast), but what I did (up to $O(q^{50})$) was verifying a possible algebraic relation between $\mu(q)$ and the classical $j$-invariant. None was found... | |
| Jan 1, 2011 at 13:24 | comment | added | Kevin Buzzard | If $\mu$ were modular then presumably there would be an algebraic relation between $\mu(q)$ and $\mu(q^n)$ for all positive integer values of $n$, the relation being of degree something like the index of $\Gamma_0(n)$ in $SL(2,Z)$ (but perhaps this isn't precisely right---the exact degree would depend on the level of $\mu$). So you could expand $\mu$ out to $O(q^1000)$ and then it would be easy to search for these relations. If it doesn't work out, i.e. if $n=5$ is OK but the others don't seem to come out, then this is evidence to suggest that $\mu$ isn't modular. | |
| Dec 31, 2010 at 13:11 | history | asked | Wadim Zudilin | CC BY-SA 2.5 |