Timeline for Interesting examples of functions that are not orthogonal to the Mobius function?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 27, 2016 at 18:50 | comment | added | Terry Tao | No, it is already biased on the numbers that are not divisible by 4. | |
| Nov 27, 2016 at 15:36 | comment | added | Kevin Smith | Something is telling me that $(-1)^n$ should have zero square free mean, but it's not something I can see how to prove. | |
| Nov 27, 2016 at 15:33 | comment | added | Kevin Smith | @Terry Tao: is $(-1)^n$ known to have a non zero mean on the squarefrees? | |
| Nov 20, 2016 at 17:28 | vote | accept | Kevin Smith | ||
| Nov 16, 2016 at 19:35 | answer | added | Asaf | timeline score: 4 | |
| Nov 14, 2016 at 22:07 | comment | added | Kevin Smith | Perhaps this was a tautological question! Thanks though. | |
| Nov 14, 2016 at 21:20 | comment | added | Terry Tao | Sure; take the left shift on the orbit closure of the Mobius sequence $\mu$, viewed as a point in $\{-1,0,+1\}^n$. | |
| Nov 14, 2016 at 21:10 | comment | added | Kevin Smith | Do any explicit examples come from positive entropy flows? I believe P. Sarnak said we know such functions exist, but perhaps he meant that $\mu$ is used in their construction. | |
| Nov 14, 2016 at 17:37 | history | edited | Kevin Smith | CC BY-SA 3.0 |
"positive", not negative!
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| Nov 14, 2016 at 17:11 | comment | added | Terry Tao | This is a tautological answer, but: one could take any function that is the product of $\mu(n)$ and an arbitrary function that has nonzero mean on the squarefree integers. | |
| Nov 14, 2016 at 15:52 | history | asked | Kevin Smith | CC BY-SA 3.0 |