Timeline for Common zeros of modular forms
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2013 at 6:12 | comment | added | Basic | Does Borcherd product type consideration say something? | |
| Mar 17, 2013 at 14:08 | comment | added | Basic | Yes, by non-trivial, I mean what Carnahan said and also to avoid oldforms. It seems that this might be a very rare phenomena. However, I do not know of any heuristics or conjectures even hinting this. | |
| Mar 17, 2013 at 9:14 | comment | added | user30035 | If you'll allow me to use oldforms (which you probably won't) then there's a trick to ensure a common zero -- because of elementary considerations involving elliptic points (which can be dressed up via a "stacky" argument to look much more fancy), if the weight of a level 1 form (eigenform or not) is not 0 mod 4 then it will have a zero at i, and if it's not 0 mod 6 it will have a zero at $\rho$. However this trick goes away if you force the conductors to go to infinity, and in this case why would one expect common zeros at all? | |
| Mar 17, 2013 at 7:16 | comment | added | S. Carnahan♦ | By "nontrivial" do you mean the list should not admit a finite partition into subsets, each having a common multiple with a zero in the same place? | |
| Mar 17, 2013 at 6:32 | history | edited | Basic | CC BY-SA 3.0 |
added 22 characters in body; edited body
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| Mar 17, 2013 at 5:09 | history | asked | Basic | CC BY-SA 3.0 |