Timeline for Simultaneous Equations Involving Power Sums
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Nov 18, 2009 at 17:43 | comment | added | Kaveh Khodjasteh | I have a simple idea that I am just sharing: Consider $f(p)=\sum_i x_i^p-\sum_i y_i^p$. Obviously $f(p)$ will eventually blow up or down for large enough p. Can we size the region [in $p$'s] over which this does not occur, if $x,y,z=\Theta(1)$ and prove that it is logarithmically small with respect to $n$? This would imply that the range of integers $k$ in those ranges of $p$ will also be limited by $log(n)$? | |
| Nov 18, 2009 at 13:00 | history | edited | David E Speyer | CC BY-SA 2.5 |
added 197 characters in body
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| Nov 18, 2009 at 12:57 | comment | added | David E Speyer | Thanks, you are both right. If I have time later today, I'll think about making the polynomial have the coefficients in question. | |
| Nov 18, 2009 at 6:11 | comment | added | Reid Barton | That is for your modification of the problem right? For the original problem I need polynomials T_l which only have coefficients of 1 and x^j, l <= j <= 2l-1? | |
| Nov 18, 2009 at 5:57 | comment | added | Greg Kuperberg | But the exponents begin at $k = \ell$, not at $k = 1$. | |
| Nov 18, 2009 at 4:41 | history | answered | David E Speyer | CC BY-SA 2.5 |