Timeline for Can we write this function as a convolution product?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 27, 2024 at 14:48 | comment | added | Steven Clark | If $b(1)\ne0$ and $b^{-1}(n)$ is the Dirichlet inverse of $b(n)$, then $a(n)$ can be evaluated as the Dirichlet convolution $a(n)=c(n) * b(n)$ where $c(n)$ is the Dirichlet convolution $c(n)=a(n) * b^{-1}(n)$ . There is no requirement for $a(n)$ to be multiplicative. | |
| Dec 27, 2024 at 8:49 | comment | added | GH from MO | Every arithmetic function $f$ can be decomposed into a convolution. For example, $f=1\ast g$, where $g:=\mu\ast f$. So you need to be more specific about what you want. | |
| Dec 27, 2024 at 7:37 | history | edited | Khadija Mbarki | CC BY-SA 4.0 | added 41 characters in body |
| Dec 26, 2024 at 19:41 | comment | added | Khadija Mbarki | Yes it is and what are these functions? | |
| Dec 26, 2024 at 19:24 | comment | added | Steven Clark | If you mean Dirichlet convolution then I believe the answer to your question is yes. | |
| Dec 26, 2024 at 8:07 | history | asked | Khadija Mbarki | CC BY-SA 4.0 |