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For the zeros in the critical band of the Riemann zeta function to determine the prime distribution, must any possible zero thereby lie in the critical line as conjectured by Riemann or they can be anywhere in principle?

bonif
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Riemann's formula is valid without RH, see here. It was proved by van Mangoldt in 1895.

Dietrich Burde
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  • So then in principle-not knowing if the hypothesis is true or not- the zeros in the critical band can be anywhere, right? – bonif Feb 28 '20 at 13:55
  • It says "involving a sum over the non-trivial zeros ρ of the Riemann zeta function." So yes. – Dietrich Burde Feb 28 '20 at 14:07