Mobius terminology

[Peter Cameron]

On Thu, Mar 10, 2005 at 07:15:45AM -0500, Emeric Deutsch wrote:
> Dear Seqfans,
> It seems that there is some confusion at some OEIS sequences 
> regarding the Mobius transform.
> Given a function g(n), defined on the positive integers, the 
> Mobius transform of g is 
>     f(n)=sum_{d|n} g(d) 
> and then, of course, g is the inverse Mobius transform of f.
> Not the other way around.
> The number theory books I have do mention Mobius pairs but do 
> not define the "Mobius transform".
> Thanks for the needed reassurance.
> Emeric

You make me nervous. This "Mobius transform" corresponds to multiplying
the Dirichlet series by the zeta function, whereas the "inverse Mobius
transform" corresponds to multiplying by the Dirichlet series of the
Mobius function.

I'd be much happier with the names "zeta transform" and "Mobius transform".

Yours, Peter Cameron.