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Do you know of any on-line references regarding relationships among the elementary number-theoretic functions?

The sort of thing I'm interested in is as at the Wikipedia page on Arithmetic Functions.

Are there any others?

Thanks.

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3 Answers 3

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There some in Abramowitz-Stegun, Handbook of Mathematical Functions.

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  • $\begingroup$ Hopefully when the <a href="dlmf.nist.gov/">DLMF</a> finally arrives, that will be an excellent replacement for the HoMF. $\endgroup$
    – Rhubbarb
    Commented Nov 13, 2009 at 18:42
  • $\begingroup$ Well, that attempt at a link didn't work, did it? Trying again: dlmf.nist.gov $\endgroup$
    – Rhubbarb
    Commented Nov 13, 2009 at 18:43
  • $\begingroup$ The website, paperback and hardback are all now available. $\endgroup$
    – Rhubbarb
    Commented Aug 17, 2010 at 0:14
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There are more than you can shake a stick at in History of the Theory of Numbers by Leonard Eugene Dickson, in Chapters II, V, X, XI, XVIII and XIX of Volume 1, especially the last. The copyright has expired and it is available for free on the web.

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There are lots of nice relations in MathWorld, but you have to search for them in the related pages. For example, if you want to find relations for zeta, or between zeta and gamma, you should visit

http://mathworld.wolfram.com/RiemannZetaFunction.html

and

http://mathworld.wolfram.com/GammaFunction.html

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