Timeline for Research of average number of equivalence classes of solutions to generalised Pell's equation
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 24, 2023 at 11:57 | comment | added | Paul Woolfer | @StanleyYaoXiao Oh, thank you. So if I take an arbitrary quadratic form of the same discriminant as $x^{2}-dy^{2}$ and find the number of representations of $N$ by both up to $GL_{2}(\mathbb{Z})$-equivalence then is it going to be the same number? | |
| Jan 23, 2023 at 15:53 | comment | added | Stanley Yao Xiao | What you call $F(M,d)$ is more or less completely understood; see for example these notes by Andrew Granville: dms.umontreal.ca/~andrew/Courses/Chapter4.pdf | |
| Jan 23, 2023 at 9:50 | comment | added | Paul Woolfer | @StanleyYaoXiao Yes, you're right. Do you know, by chance, any good papers on the way this number of representations is counted? I want to have a deeper understanding. | |
| Jan 23, 2023 at 1:54 | comment | added | Stanley Yao Xiao | If I am understanding correctly, are you asking for the number of representations of $N$ by $f$ up to $\text{GL}_2(\mathbb{Z})$-equivalence? If so, then this is basically just the divisor function on $N$ provided that all of the prime factors of $N$ either split in the quadratic field or have even multiplicity. | |
| S Jan 22, 2023 at 22:59 | review | First questions | |||
| Jan 23, 2023 at 3:27 | |||||
| S Jan 22, 2023 at 22:59 | history | asked | Paul Woolfer | CC BY-SA 4.0 |