Timeline for Sums of two squares: What is known about the distribution of r(n)?
Current License: CC BY-SA 3.0
10 events
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| Feb 13, 2013 at 14:47 | history | edited | Yuri Gurevich | CC BY-SA 3.0 |
Final thanks
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| Feb 10, 2013 at 16:49 | comment | added | GH from MO | Your conjecture is false, see the Added part of my response. | |
| Feb 10, 2013 at 16:20 | comment | added | Noam D. Elkies | [Greg Martin is right; my comment from yesterday (deleted, but appended here) is correct but answers a different question.]$$ $$ "It's known that $\sum_{n<x} r(n) = \pi x + O(x^\theta)$ for some $\theta$ slightly less than $1/3$. (Getting $1/3$ is standard; the conjecture is that it's true for any $\theta > 1/4$.) That's more than enough to get $\sum_{n=a}^{a+\Theta(\sqrt{a})} r(n) > 0$ for large $a$." | |
| Feb 10, 2013 at 7:17 | answer | added | Greg Martin | timeline score: 8 | |
| Feb 10, 2013 at 4:39 | history | edited | Yuri Gurevich | CC BY-SA 3.0 |
Narrowed the question to a specific conjecture.
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| Feb 9, 2013 at 18:14 | history | edited | Yuri Gurevich |
edited tags
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| Feb 9, 2013 at 18:06 | history | edited | Yuri Gurevich | CC BY-SA 3.0 |
Narrowing the question
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| Feb 8, 2013 at 20:57 | answer | added | GH from MO | timeline score: 11 | |
| Feb 8, 2013 at 19:23 | comment | added | Abhinav Kumar | The average value is $\pi$, as you can convince yourself by counting the integer points inside a large circle. For more information, see mathworld.wolfram.com/SumofSquaresFunction.html or (say) a book on analytic number theory ... | |
| Feb 8, 2013 at 19:06 | history | asked | Yuri Gurevich | CC BY-SA 3.0 |