Talk:Prime Number Theorem

Revision as of 12:15, 29 June 2006 by Fedja (talk | contribs)

This proof is much harder than the proof using the zeta function. To do that, you just have to show that there are no zeros on the one line. --ComplexZeta 12:48, 29 June 2006 (EDT)

Hmmm... The fact that zeta-function has no zeroes with $\Re z=1$ will be used here for sure but it is not the end of the story: to the best of my knowledge, to finish, one has to use either Riemann's explicit formula for $\pi(x)$, or some complex analysis trick, or some Tauberian theorem. I was inclined to use the last approach because I find it a bit more natural than the other two. But, perhaps, you know some clever shortcut I am unaware of. If so, I'll be most grateful if you write the proof you know. --Fedja 13:15, 29 June 2006 (EDT)

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