Re: [PrimeNumbers] RH fun
- Well ok, I think we've boiled it down to explaining the obvious by now.
Yes, a non-critical zero makes a larger contribution. It's not
necessarily the end of the world though, it all depends what you're
trying to prove.
On Wed, Aug 06, 2003 at 09:58:29AM +0100, Jon Perry wrote:
> The fundamental stumbling block in Riemanns's pi(x) estimate is the presence
> of the
> terms. Riemann claims that these oscillate in sign, and therefore
> effectively cancel each other out, and do not need to be included in the
> final pi(x) sum. One of his reasons for the claim is the Riemann Hypothesis.
> But if a root does not lie on the critical line, then a contributing factor
> is x^(1/4) say, not x^(1/2), which dominates the sum, and prevents the
> cancelling out process, because as x grows, this one term grows quicker than
> the others.