Timeline for Why are there usually an even number of representations as a sum of 11 squares
Current License: CC BY-SA 2.5
15 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 20, 2010 at 19:25 | comment | added | Kevin O'Bryant | @Sergei: I'm intrigued now. How did you deduce that $n$ must have one of those forms? | |
| Jun 20, 2010 at 14:43 | vote | accept | Kevin O'Bryant | ||
| Jun 19, 2010 at 22:27 | answer | added | Greg Kuperberg | timeline score: 4 | |
| Jun 19, 2010 at 5:46 | comment | added | Sergei Ivanov | @Kevin: I assumed $n\equiv 3$ mod 8 | |
| Jun 19, 2010 at 1:51 | answer | added | paul Monsky | timeline score: 15 | |
| Jun 18, 2010 at 22:39 | comment | added | Kevin O'Bryant | @Sergei: $n=20$ has the unique rep $(a,b,c)=(2,2,1)$, but isn't of either of those forms. | |
| Jun 18, 2010 at 18:30 | comment | added | Sergei Ivanov | If I am not mistaken, the odd number of representations as $a^2+2b^2+8c^2$ can only happen for $n$ of the form $a^2+2b^2$ or $a^2+2pb^2$ where $a,b$ are positive integers and $p$ is a prime number which is 1 mod 4. Is there any chance that the set of $n$'s representable this way has zero density? | |
| Jun 17, 2010 at 21:00 | answer | added | Will Jagy | timeline score: 4 | |
| Jun 17, 2010 at 18:50 | history | edited | Will Jagy | CC BY-SA 2.5 |
added 53 characters in body; edited tags
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| Jun 17, 2010 at 11:50 | comment | added | Kevin O'Bryant | @Hugo: You are understanding the question correctly. As you go out further and further, that percentage keeps falling, albeit slowly. I'm asking if it gets to zero, and if so, why. | |
| Jun 17, 2010 at 11:48 | comment | added | Kevin O'Bryant | @Sune: I am not assuming $x_i$ non-increasing. So, for example, 3 has $\binom{11}{3}=165$ representations as a sum of 11 squares. | |
| Jun 17, 2010 at 10:26 | comment | added | Hugo van der Sanden | What do you mean by "so few"? Numerically, I find 6,802 of the first 20,000 $n \equiv 3 \bmod 8$ have an odd number of representations as $x_0^2+2x_1^2+8x_3^2$. Are you asking why this is 34% rather than 50%, or am I misunderstanding the question? | |
| Jun 17, 2010 at 6:02 | comment | added | Sune Jakobsen | Are you assuming that $x_i$ is non-increasing? | |
| Jun 17, 2010 at 5:32 | history | asked | Kevin O'Bryant | CC BY-SA 2.5 |