Timeline for Siegel's bad character
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 3, 2020 at 8:31 | answer | added | Franz Lemmermeyer | timeline score: 1 | |
| Apr 3, 2020 at 4:29 | comment | added | GH from MO | I added a remark to your other post. Note also that the ring class group there has $f+1$ elements, so it has $f+1$ characters. Siegel elaborates on the quadratic characters (also known as genus characters). Nontrivial quadratic characters exist if and only if $f+1$ is even (i.e. $f$ is odd). | |
| Apr 2, 2020 at 17:17 | comment | added | Shimrod | @GHfromMO How then do you explain the following puzzling phenomenon: in this question I found that each class contains a proper fractional ideal with norm equal to $1$. But it follows from this that the value of the character is always $1$. This does not make sense to me. | |
| Apr 2, 2020 at 14:52 | comment | added | GH from MO | The ring class group is associated to an order $\mathcal{O}$ of a number field. It equals the multiplicative group of invertible fractional ideals in $\mathcal{O}$ modulo the subgroup of invertible principal fractional ideals in $\mathcal{O}$. In an imaginary quadratic number field, there is a unique order of conductor $f$, and this gives rise to the ring class group of conductor $f$. | |
| Apr 2, 2020 at 12:36 | comment | added | user131781 | I am quite relaxed, thank you very much. | |
| Apr 2, 2020 at 12:31 | comment | added | Francois Ziegler | @user131781 Relax! | |
| Apr 2, 2020 at 12:25 | comment | added | Shimrod | @GHfromMO Where can I find definition of the ring class group of conductor $f$? | |
| Apr 2, 2020 at 12:17 | comment | added | GH from MO | "Gruppe der Ringklassen mit dem Führer $f$" means "ring class group of conductor $f$". The modern point of you is that you divide the idele class group by the relevant open subgroup, and you consider the characters of the quotient group. There are many books on the subject, e.g. Weil: Basic number theory, Neukirch: Algebraic number theory etc. | |
| Apr 2, 2020 at 12:15 | history | edited | Shimrod | CC BY-SA 4.0 |
added 127 characters in body
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| Apr 2, 2020 at 11:59 | history | edited | Shimrod | CC BY-SA 4.0 |
added 13 characters in body
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| Apr 2, 2020 at 11:59 | comment | added | Lior Silberman | Am I the only one who expected a biographical discussion of Carl Ludwig Siegel? | |
| Apr 2, 2020 at 11:58 | history | asked | Shimrod | CC BY-SA 4.0 |