Timeline for Probability a polynomial has a root which is a root of unity
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2014 at 9:21 | vote | accept | Simd | ||
| May 29, 2014 at 20:42 | comment | added | user21349 | @JonPeterson: The fact that these two probabilities are equal is not the same as saying doubling is correct. Some polynomials have both $1$ and $-1$ as roots, so the probability that one or the other is a root is less than double the probability that one is a root. However, as I argued in a comment, the probability that both are roots is small for large $n$. | |
| May 29, 2014 at 16:35 | comment | added | Jon Peterson | Note that the probability that 1 is a root is equal to the probability that -1 is a root. This is easily seen by the fact that $P(1)$ and $P(-1)$ have the same distribution since the random coefficients $c_i$ are such that $-c_i$ has the same distribution as $c_i$. This explains why you would double the probability that 1 is a root in your above calculations. | |
| May 28, 2014 at 19:00 | history | edited | user21349 | CC BY-SA 3.0 |
added 14 characters in body
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| May 28, 2014 at 18:41 | history | answered | user21349 | CC BY-SA 3.0 |