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Can anyone post a self-contained reference concerning the extension of the Euler phi function to number rings and its basic properties (reminiscent of those that the classic Euler phi function has)? Such properties have been shown and proved for this function in a few posts here on MathOverflow.

One such post: Generalized Euler Phi Function

This generalized phi function has also appeared in several papers concerning distribution of prime ideals without any reference to its properties. The one reference that I did have was from Ian Kiming's Algebraic Number Theory notes, and the link to this seems to be gone now.

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    $\begingroup$ This function is defined and explored in some exercises in Borevich and Shafarevich's Number Theory: exercises 4 to 7 on pages 231 and 232. Although you may feel there is a lack of references on this topic, is there something about this function that you want to know but can't work out for yourself? $\endgroup$ – KConrad Mar 13 at 8:19
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    $\begingroup$ Similar question at mathoverflow.net/questions/52718/generalized-euler-phi-function. $\endgroup$ – Richard Stanley Mar 13 at 13:24
  • $\begingroup$ To KConrad: I'd like to have a reference with this function and its basic properties worked out so I can quote it in the bibliography to one of my papers that has just been accepted. I had been quoting Kiming until the link to his notes went dead. Thanks for asking! $\endgroup$ – BDS Mar 13 at 15:03

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