Timeline for counting points on unit sphere mod p
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Jul 2, 2018 at 10:15 | answer | added | Gro-Tsen | timeline score: 9 | |
| Jul 2, 2018 at 4:36 | history | edited | Alexey Ustinov | CC BY-SA 4.0 |
deleted 2 characters in body
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| Jul 2, 2018 at 4:35 | answer | added | Alexey Ustinov | timeline score: 1 | |
| Feb 26, 2018 at 16:30 | history | edited | Adam P. Goucher | CC BY-SA 3.0 |
s/thru/, \dots, /
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| Jul 16, 2013 at 11:40 | history | edited | john mangual | CC BY-SA 3.0 |
typo
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| Jul 10, 2013 at 23:31 | comment | added | john mangual | The distribution of quadratic forms $\mod p$ seems intimately tied with quadratic reciprocity math.ucsd.edu/~kedlaya/2012s.pdf | |
| Jul 10, 2013 at 14:57 | comment | added | john mangual | These solutions are quite varied, using Fourier analysis, Probability and trees and quadratic reciprocity. Doesn't Hensel's lemma get you integer solutions to quadratic forms as well? | |
| Jul 10, 2013 at 14:24 | comment | added | Noam D. Elkies | Yet another MO source for counting solutions of $\sum_{i=1}^n x_i^2 \equiv 1 \bmod p$: mathoverflow.net/questions/1420/… | |
| Jul 10, 2013 at 14:00 | comment | added | john mangual | @AbhinavKumar I take it with Chinese Remainder and Hensel's lemma, formulas like these should exist for any quadratic form. It also means the solution sets are quite regular. Thank you. | |
| Jul 10, 2013 at 13:47 | history | edited | john mangual | CC BY-SA 3.0 |
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| Jul 10, 2013 at 13:41 | comment | added | Noam D. Elkies | Typo: the formula for a circle should be $x^2+y^2=1$ (or $\equiv 1$), not $x^2+y^2+z^2=1$. | |
| Jul 10, 2013 at 13:40 | comment | added | Noam D. Elkies | For the number of solutions mod $p$ to $\sum_{i=1}^n x_i^2 = 1$, see mathoverflow.net/questions/69576/sum-of-squares-modulo-a-prime | |
| Jul 10, 2013 at 13:28 | comment | added | Abhinav Kumar | The formula must be a multiplicative function, by CRT (since you're counting number of solutions to some congruence). So you need to compute the number of solutions mod prime powers $p^k$. Do this for $k = 1$ and then use Hensel (if $p = 2$, you might have to start with $k = 3$). This sort of "mass" formula is common when you consider representation numbers of quadratic forms. For instance, see the book "Rational quadratic forms" by Cassels. | |
| Jul 10, 2013 at 13:06 | comment | added | john mangual | I wonder if these functions have appeared in the "serious" number theory literature and why. I had thought of this while trying to answer mathoverflow.net/questions/136131/calculus-over-finite-fields on this site. | |
| Jul 10, 2013 at 13:05 | history | edited | john mangual | CC BY-SA 3.0 |
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| Jul 10, 2013 at 12:45 | history | asked | john mangual | CC BY-SA 3.0 |