# Difference between revisions of "Talk:Prime Number Theorem"

ComplexZeta (talk | contribs) |
|||

Line 1: | Line 1: | ||

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. --[[User:ComplexZeta|ComplexZeta]] 12:48, 29 June 2006 (EDT) | 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. --[[User:ComplexZeta|ComplexZeta]] 12:48, 29 June 2006 (EDT) | ||

+ | |||

+ | Hmmm... The fact that zeta-function has no zeroes with <math>\Re z=1</math> 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 <math>\pi(x)</math>, 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. --[[User:Fedja|Fedja]] 13:15, 29 June 2006 (EDT) |

## Revision as of 12:15, 29 June 2006

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 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 , 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)