Timeline for How to calculate genus number of number field using sage?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 30, 2021 at 18:35 | vote | accept | SUNIL PASUPULATI | ||
| Aug 28, 2021 at 12:33 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
edited tags; edited title
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| Aug 28, 2021 at 12:16 | answer | added | Carl-Fredrik Nyberg Brodda | timeline score: 2 | |
| Aug 27, 2021 at 8:34 | comment | added | Carl-Fredrik Nyberg Brodda | For example, you can take $d = 2,3,5,7,10,...$ for your problem, i.e. the class and genus number of e.g. $\mathbf{Q}(\sqrt{10})$ are equal (both are $2$ in this case). | |
| Aug 27, 2021 at 8:18 | comment | added | Carl-Fredrik Nyberg Brodda | The genus number of quadratic number fields over $\mathbf{Q}$ was computed by Hasse (J. Math. Soc. Japan 3, 1951); he shows the genus number of $\mathbf{Q}(\sqrt{d})$ is $2^{r-1}$, where $r$ is the number of distinct prime divisors of $d$. | |
| Aug 27, 2021 at 4:34 | history | asked | SUNIL PASUPULATI | CC BY-SA 4.0 |