I have been studying the continuation of the Riemann zeta function $\zeta(s)$ for the past while. I can prove that all the zeroes must lie in the critical strip.I am currently in the process of using this to prove the Prime Number Theorem. Of course I want to prove it analytically, and would like to know which proof would be best suited for somebody of an intermediate understanding of complex analysis and number theory. I have had a look at Newmans proof, and see that it requires knowledge of laplace transform and his analytic theorem. Would understanding these concepts be less effort than proving the PNT by more 'traditional' means?
2026-04-04 13:50:00.1775310600
Out of all the proofs of the PNT, which one is the most accessible?
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You can find the background of the proof of PNT and an elementary proof of i in this article http://www.math.columbia.edu/~goldfeld/ErdosSelbergDispute.pdf