Date: Jan 5, 2013 11:06 AM
Author: David Bernier
Subject: Re: equivalence of truth of Riemann hypothesis

On 01/05/2013 09:55 AM, Jean Dupont wrote:> In the book "Math goes to the movies" it is stated that the truth of the Riemann hypothesis is equivalent to the following statement:> $\exists C: \forall x \in \mathbb{N}_0: \left|\pi(x)-\operatorname{li}(x)\right| \leq C \sqrt{x} \log(x)$>> Is this correct?>> thanks> jeanThe movie "A Beautiful Mind" about John Nash is now on Youtube:< http://www.youtube.com/watch?v=OOWT1371DRg > .I think John Nash in the movie or in reality tried to makehead-way on the Riemann Hypothesis ...David BernierP.S. I'm afraid I can't read Tex or Latex ...  But, please see "error term" in Prime Number Theorem, here:primepages, 1901 von Koch result:< http://primes.utm.edu/notes/rh.html >I trust PrimePages.  Also, Schoenfeld(1976) explicit bound:< http://en.wikipedia.org/wiki/Riemann_hypothesis > .