Timeline for Cyclotomic polynomials: $\Phi_n(p)$ is like $p^{\phi(n)}$ for big enough $p$, right?
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2015 at 18:20 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
added 8 characters in body
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| Oct 23, 2015 at 18:08 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
more acknowledgment and refined answer
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| Oct 23, 2015 at 17:18 | answer | added | Gerhard Paseman | timeline score: 2 | |
| Oct 22, 2015 at 18:57 | comment | added | Wolfgang | @FanZheng Concerning the question of tags: as a suitable tag for all "cyclotomic-polynomials" stuff, one may also use the existing "roots-of-unity" tag. | |
| Oct 21, 2015 at 19:48 | comment | added | Gerhard Paseman | I think students should note the following: I had some of the clues posted above before seeing Jameson's writeup, especially about using inversion and noting the improvement using prime powers. I didn't have 1.19, but might have developed it. The moral is to believe in the clues: I am surprised I got that close to a solution from just quick observations. Gerhard "Off To Observe Some More" Paseman, 2015.10.21 | |
| Oct 21, 2015 at 19:16 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
Included interpretation of Jameson's writeup.
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| Oct 21, 2015 at 5:34 | comment | added | Gerry Myerson | No. At $n=105$, I get 1.682. Similarly for other products of three odd primes. I wouldn't be surprised if also for products of 5, 7, etc. odd primes. Maybe other numbers as well – long time since I looked at it. | |
| Oct 20, 2015 at 19:20 | comment | added | Gerhard Paseman | @Gerry , some of us would like to know more. In particular, is $\Phi_n(2)/2^{\phi(n)} \gt 3/2$ only for odd primes $n$? Gerhard "Almost Read Gerry's (Almost) Paper" Paseman, 2015.10.20 | |
| Oct 20, 2015 at 18:40 | vote | accept | Gerhard Paseman | ||
| Oct 20, 2015 at 12:14 | comment | added | Gerry Myerson | The set $\{\,\phi_n(2)/2^{\phi(n)}:n=1,2,\dots\,\}$ has some interesting structure. I almost wrote a paper about it once. | |
| Oct 20, 2015 at 7:27 | comment | added | joro | Shouldn't this work for real p large enough? | |
| Oct 20, 2015 at 6:59 | history | edited | Gerhard Paseman | CC BY-SA 3.0 |
added 19 characters in body
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| Oct 20, 2015 at 4:05 | answer | added | Geoff Robinson | timeline score: 6 | |
| Oct 20, 2015 at 3:37 | answer | added | Venkataramana | timeline score: 17 | |
| Oct 20, 2015 at 3:34 | comment | added | Fan Zheng | I haven't found any discussion on that in meta, and I don't think tag search supports wildcard yet: "cyclo*m*" turns up nothing. Fan "Not Implemented" Zheng | |
| Oct 20, 2015 at 3:28 | comment | added | Gerhard Paseman | Indeed. Perhaps this has been discussed in meta already. Although I can see tag-fracturing as a danger, I can also see the use of wildcard searches for tag values. Gerhard "We Can Work Around This" Paseman, 2015.10.19 | |
| Oct 20, 2015 at 3:25 | comment | added | Fan Zheng | A search using the key word "cyclotomic" turns up three tags "cyclotomic-integers", "cyclotomic-fields" and "cyclotomic-integer". I'm suggesting a merger to something like "cyclotomy". Fan "Better Tags" Zheng | |
| Oct 20, 2015 at 3:17 | comment | added | Gerhard Paseman | I think we need a "cyclotomic-polynomials" tag. Gerhard "Second Question On This Account" Paseman, 2015.10.19 | |
| Oct 20, 2015 at 3:13 | history | asked | Gerhard Paseman | CC BY-SA 3.0 |