Timeline for Possible relation for Euler's Totient
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 11, 2011 at 14:56 | history | edited | Damien Zammit | CC BY-SA 3.0 |
added 61 characters in body; added 24 characters in body
|
| Jul 11, 2011 at 14:03 | comment | added | Todd Trimble | I'm having some trouble believing this is originally due to W. Schramm. It looks awfully similar to a formula like $\phi(n) = \sum_{d|n} (n/d)\mu(d)$, where $\mu(d)$ is recast as the sum of primitive $d^{th}$ roots of unity. Am I making a mistake? | |
| Jul 11, 2011 at 13:39 | history | edited | Damien Zammit | CC BY-SA 3.0 |
added 43 characters in body
|
| Jul 11, 2011 at 13:31 | history | edited | Damien Zammit | CC BY-SA 3.0 |
More indepth account of what I did
|
| Jul 11, 2011 at 12:24 | history | edited | Damien Zammit | CC BY-SA 3.0 |
Realised it is not a recurrence relation
|
| Jul 11, 2011 at 11:45 | comment | added | Damien Zammit | With or without the minus sign as far as I can tell is mathematically equivalent, but has to do with the choice of 'polarity' of the Fourier transform of the gcd function described in W. Schramm's paper above. | |
| Jul 10, 2011 at 20:05 | comment | added | Michael Hardy | I saw "Schramm" and thought "Oded Schramm" (maybe that's silly, given the topic?), but this is Wolfgang Schramm: emis.ams.org/journals/INTEGERS/papers/i50/i50.pdf | |
| Jul 10, 2011 at 13:18 | comment | added | Gerald Edgar | What's with the minus sign inside the cosine? | |
| Jul 10, 2011 at 12:23 | comment | added | Gjergji Zaimi | This is a relation, undoubtedly, but it's he "recurrence" part that's missing. | |
| Jul 10, 2011 at 11:32 | comment | added | Wadim Zudilin | Can you give a single example when the relation of type $f(n,n)=\sum_{i<n}c_if(i,n)+g(n)$ could determine $f(n,n)$? There is no control of $f(i,n)$ for $i\ne n$, but even if it were, you would require at least one more recursion plus initial conditions. | |
| Jul 10, 2011 at 10:45 | history | asked | Damien Zammit | CC BY-SA 3.0 |