Timeline for Many representations as a sum of three squares
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 9, 2015 at 20:50 | comment | added | Adam Sheffer | Thank you again Lucia. Hopefully I'm done with these questions. | |
| Sep 9, 2015 at 20:29 | comment | added | Lucia | @AdamSheffer: In these arguments you can easily restrict $d$ to be in any progression that you want, and the result carries through. The constants in the bound may depend on the progressions. | |
| Sep 9, 2015 at 19:53 | comment | added | Adam Sheffer | Actually, that is for 0, 4, and 7. | |
| Sep 9, 2015 at 19:51 | comment | added | Adam Sheffer | I have yet another question about this. Sorry for the multiple questions. In the formulas for $r_3(n)$ and $r^*_3(n)$, the value is zero if $n\equiv 7 mod 8$. How do I know that there is a value of $n$ for which both $L(1,\chi_d)$ is large and $n\not\equiv 7 mod 8$? | |
| Sep 7, 2015 at 23:27 | vote | accept | Adam Sheffer | ||
| Sep 7, 2015 at 23:25 | comment | added | Lucia | @AdamSheffer: Nothing wrong with what you wrote; but note that if $n=a^2+b^2+c^2$ then $n$ is the square of the distance. (i.e. you just have a scaling issue in what you wrote) | |
| Sep 7, 2015 at 23:22 | comment | added | Adam Sheffer | Thank you both! I appreciate the help. If the solution is close to $\sqrt{n}$, I wonder what is wrong with the following argument that implies $n$. Consider the set of points in ${\mathbb Z}^3$ with all of their coordinates between $-n$ and $n$. A number with many representations corresponds to a sphere around the origin containing many points. Each point $a$ has a distance of $\sqrt{a_x^2+a_y^2+a_z^2}$ from the origin. Since there are about $n^3$ points and about $n^2$ distances, there must be a sphere with at least $n$ points (i.e., a distance with at least $n$ representations). | |
| Sep 7, 2015 at 22:52 | comment | added | GH from MO | No, it is fun! Let me upvote you... | |
| Sep 7, 2015 at 22:47 | comment | added | Lucia | @GH from MO: That's too bad -- one of us could have saved their energy. | |
| Sep 7, 2015 at 22:46 | comment | added | GH from MO | You beat me by one minute... | |
| Sep 7, 2015 at 22:44 | history | answered | Lucia | CC BY-SA 3.0 |