Additive sequences

[Edwin Clark]

The terms additive function (resp., multiplicative function) are well 
established in the number theory literature with the definitions

a(n*m) = a(n) + a(m) whenever gcd(n,m) = 1. 

(resp.,a(n*m) = a(n)*a(m) whenever gcd(n,m) = 1.)

See, e.g., Harold Shapiro's Introduction to the Theory of Numbers

or just Google:  number theory "additive function"

--Edwin

On Wed, 20 Sep 2006 franktaw at netscape.net wrote:

> I'm not sure it's a good name either.  My own preference
> would be "log multiplicative", since when you exponentiate
> such a sequence you get a multiplicative sequence.
> 
> But "additive" is, as stated, already in use in the database.
> Barring a finding of the form "there's a lot of literature on
> these, and they're called X", it isn't going to change.
> 
> Franklin T. Adams-Watters
> 
> 
> -----Original Message-----
> From: ralf at ark.in-berlin.de
> 
> You wrote
> > There was some discussion on this list a while back
> > about what to call sequences where
> > a(n*m) = a(n) + a(m) whenever gcd(n,m) = 1.
> > I don't think there was any consensus reached,
> > but one of the possibilities, "additive", was and is
> > in use in the database, so I guess it wins by default.
> 
> I'm not sure if this is a good name, as it implies having
> something to do with 'additive number theory' which is
> way off here.
> 
> (I'm not against, just count it as abstention)
> 
> 
> Regards,
> ralf
> 
> 
> 
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---------------------------------------------------------
  W. Edwin Clark, Math Dept, University of South Florida
           http://www.math.usf.edu/~eclark/
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