Timeline for On $\eta(6z)\eta(18z)$ and the splitting / modularity of $x^3 - 2$
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 20, 2016 at 8:39 | vote | accept | Serendipity | ||
| May 12, 2016 at 14:10 | comment | added | Jeremy Rouse | Yes, that's right - only odd dihedral representations. | |
| May 12, 2016 at 13:48 | comment | added | David E Speyer | More precisely, dihedral extensions where complex conjugation acts by an element of determinant $-1$ -- otherwise you have to deal with ray class characters of real quadratic fields and you get Maas forms instead of modular forms. | |
| May 12, 2016 at 13:47 | comment | added | Jeremy Rouse | I believe this method will work for all dihedral representations, and no others. The rough idea is that the space of weight 1 cusp forms spanned by differences of theta series should be decomposable into linear combinations of forms obtained from ray class characters of imaginary quadratic fields - these correspond by class field theory to dihedral extensions of $\mathbb{Q}$. | |
| May 12, 2016 at 13:38 | comment | added | Serendipity | Thanks! It seems that all such "classic" solutions I have seen involve theta series. Will it work for all $S_3$ representations (or maybe even more)? | |
| May 12, 2016 at 13:24 | history | answered | Jeremy Rouse | CC BY-SA 3.0 |