Timeline for Asymptotic formula for the number of ways to write a number as the sum of $k$ triangular numbers
Current License: CC BY-SA 3.0
6 events
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| Apr 1, 2015 at 9:09 | answer | added | Kimball | timeline score: 1 | |
| Sep 1, 2014 at 3:43 | answer | added | H.Flip | timeline score: 0 | |
| Aug 31, 2014 at 1:42 | history | edited | José Hdz. Stgo. | CC BY-SA 3.0 |
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| Aug 30, 2014 at 23:27 | comment | added | Lucia | Multiply $n$ by $8$ and add $k$. Thus the problem is equivalent to representing $8n+k$ as a sum of odd squares, and all that you want to know has been worked out. For $k\ge 5$ there is no problem with using the circle method (or modular forms) -- the asymptotic is about $C(n) n^{k/2-1}$, where $C(n)$ is bounded above and below. For $k=4$, use Jacobi's work on sums of four squares. For $k=3$, Gauss related sums of three squares with class numbers. | |
| Aug 30, 2014 at 21:45 | history | edited | GH from MO |
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| Aug 30, 2014 at 21:32 | history | asked | Mayank Pandey | CC BY-SA 3.0 |