Date: Jan 5, 2013 2:41 PM
Author: David Bernier
Subject: Re: equivalence of truth of Riemann hypothesis

On 01/05/2013 11:30 AM, Jean Dupont wrote:> Op zaterdag 5 januari 2013 17:06:11 UTC+1 schreef David Bernier het volgende:>> 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>>>>> jean>>>>>>>> The 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 make>>>> head-way on the Riemann Hypothesis ...>>>>>>>> David Bernier>>>>>>>> P.S. I'm afraid I can't read Tex or Latex ...> just copy/paste the line>> exists C: \forall x \in \mathbb{N}_0: \left|\pi(x)-\operatorname{li}(x)\right| \leq C \sqrt{x} \log(x)>> in the box shown on the following web  page and press render:> http://itools.subhashbose.com/educational-tools/latex-renderer-n-editor.html>>> jeanYes, I believe that is equivalent to the Riemann Hypothesis.I think that follows quite easily from Schoenfeld's resultof 1976, which is stated at Wikipedia's article on RH:http://en.wikipedia.org/wiki/Riemann_hypothesisP.S.  What is N_0 , 'N' being similar to '|N'   ?