sppose that $\sigma_k:\mathbb N \longrightarrow \mathbb R$ is a function such that $\sigma_k(n)=\sum_{d|n}d^k$. $\rho_k:\mathbb N \longrightarrow \mathbb R$ is a function such that $\rho_k\ast \sigma_k=\delta$. find a formula for $\rho_k$.($\frac{100}{6}$ points)
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Tags: function, number theory proposed, number theory
mahanmath
09.08.2010 13:10
This is what I know about it :
Stranger8
19.03.2016 17:25
Sorry ,can you tell me what does the $\rho_k\ast \sigma_k=\delta$ mean please
mihajlon
19.03.2016 19:45
Stranger8 wrote: Sorry ,can you tell me what does the $\rho_k\ast \sigma_k=\delta$ mean please Anyone?
babu2001
21.03.2016 17:47
Am I mistaking the problem??? As the required function can be defined as the inverse of the sigma function given for each natural no. n
Justanaccount
22.01.2022 15:31
What does the delta function mean in the RHS? Is it an arbitrary function?
CANBANKAN
26.01.2022 10:13
I think $\delta(1)=1$ and $\delta(x)=0$ for all $x>1$.