(adsbygoogle = window.adsbygoogle || []).push({}); Help with Mobius Inversion in "Riemann's Zeta Function" by Edwards (J to Prime Pi)

Can someone please add more detail or give references to help explain the lines of math in "Riemann's Zeta Function" by Edwards.

At the bottom of page 34 where it says "Very simply this inversion is effected by performing ...", the two lines of math that follow could do with a few more lines perhaps to make it clear enough for me to understand. I am already lost on the first line. One line or two before this might be all the help that I need.

I have been studying up on Mobius inversion, but with all my uni books and online references, I am having great difficulty in finding examples of the use of the inversion in the case of inverting a summation over the integers. For example in "Elementary Number Theory" by Rosen, I see the definition of the Mobius Function, some proofs of properties of the Mobius Function, a proof of the Mobius Inversion Formula, and then some identities that follow by immediate application of the inversion formula; but I don't see an inversion of summations like the J to Prime Pi.

Perhaps someone knows some chapters of books or papers for me to read. What I would really like to do is find a bunch of examples and questions to answer where I have to invert some 'sums over the integers' of various functions to give experience on the techniques necessary to achieve such a thing. I would need solutions too but the forum could help with that I suppose.

I understand that the Mobius Inversion only inverts 'summatory functions' summing over the divisors of a number.

I have a particular 'summation over the integers' of a function to invert if possible but I would like to have a go at it myself first.

Thanks.

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# Help with Mobius Inversion in Riemann's Zeta Function by Edwards (J to Prime Pi)

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