Timeline for Class number for binary quadratic forms discriminant $\Delta$ to class number $\mathbb Q(\sqrt \Delta)$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 25, 2014 at 15:24 | comment | added | Will Jagy | Getting easier: if the principal form does not represent minus one, call these forms (classes) $1$ and $-1.$ Dirchlet's method for binary form composition shows immediately that $$ -1 \circ \langle A,B,-C \rangle = \langle -A,B,C \rangle. $$ These two forms $\langle A,B,-C \rangle ,$ $ \langle -A,B,C \rangle. $ are guaranteed distinct classes, the field mapping says they must go to the same place. | |
| Jun 24, 2014 at 17:27 | vote | accept | Will Jagy | ||
| Jun 23, 2014 at 16:28 | vote | accept | Will Jagy | ||
| Jun 24, 2014 at 17:26 | |||||
| Jun 23, 2014 at 16:26 | comment | added | Will Jagy | Thank you. I paraphrased my sources, it is probably my fault. Final bit, For a number such as $210 \equiv 2 \pmod 4,$ my only choice is to check discriminant $840,$ and indeed then get my "form class number" as 8. Does that sound right, for $\mathbb Q ( \sqrt n)$ with $n \equiv 2,3 \pmod 4,$ I check forms of discriminant $4n?$ Pasting 210 output into question... | |
| Jun 23, 2014 at 13:47 | history | answered | Jeremy Rouse | CC BY-SA 3.0 |