Timeline for Field of minimum discriminant of a given degree
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 21, 2019 at 8:25 | comment | added | Joachim König | I would see a certain (very shaky) evidence that $S_n$ has a decent chance of claiming the lowest $|D|$ as long as $n$ is prime. That's because in that case $S_n$ is the only group with a transposition, and then Malle's conjecture on discriminant says that $S_n$-discriminants should be of positive density in $\mathbb{N}$, while all others should not be - of course, that's a statement about asymptotics, not about smallest values, so it might not be worth much either. As soon as $n$ is not prime, there are other groups containing transpositions, which then should "rival" the $S_n$-discriminants. | |
| Jan 27, 2019 at 4:08 | comment | added | Stanley Yao Xiao | That is very interesting... do you suspect that $g(n) = (1 - (-1)^n)/2$ for $n \geq 3$? | |
| Jan 26, 2019 at 3:32 | history | answered | Noam D. Elkies | CC BY-SA 4.0 |