Timeline for Can something finite over $\mathbb{C}(q)$ be a modular form?
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| Jul 22, 2016 at 7:17 | comment | added | Noam D. Elkies | Likewise $p=3$. But for $p=2$ (respectively $p=3$) the ring of modular forms is generated not by $E_4$ and $E_6$ but by $a_1$ (resp. $a_2$) and $\Delta$. | |
| Jul 22, 2016 at 1:14 | comment | added | Felipe Voloch | @KevinBuzzard Properly formulated, it works in char 2 also. For a discussion of the theta function see the paper by D. Thakur J. Number Theory 58 (1996) 60-63 which follows mine (in several ways) | |
| Jul 21, 2016 at 22:42 | comment | added | Kevin Buzzard | I think that for $p=2$ it has transcendence degree 0 :-) But you can use Delta too, right? The transcendence of $q$ -- I knew that this was relevant but I didn't know it was proved -- thanks for the reference! | |
| Jul 21, 2016 at 22:10 | history | answered | Felipe Voloch | CC BY-SA 3.0 |