Timeline for A conjectural formula for the class number of the field $\mathbb Q(\sqrt{-p})$ with $p\equiv3\pmod8$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 7, 2019 at 0:56 | answer | added | XIP | timeline score: 14 | |
| Aug 6, 2019 at 11:55 | comment | added | François Brunault | Assuming the analytic class number formula this should be provable using just trigonometry. E.g. one could expand $1/\sin(2\pi x/p) = -2i\zeta_p^x /(1-\zeta_p^{2x}) = (2i\zeta_p^x/p) \sum_{y=1}^{p-1} y \zeta_p^{2xy}$. | |
| Aug 6, 2019 at 8:48 | comment | added | Zhi-Wei Sun | Via Galois theory and quadratic Gauss sums, we see that the right-hand side of the formula is a rational number. | |
| Aug 6, 2019 at 8:29 | history | asked | Zhi-Wei Sun | CC BY-SA 4.0 |