Date: Jan 5, 2013 3:36 PM
Author: Jean Dupont
Subject: Re: equivalence of truth of Riemann hypothesis

Op zaterdag 5 januari 2013 20:41:23 UTC+1 schreef David Bernier het volgende:> 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> > >>> > > jean> > > > Yes, I believe that is equivalent to the Riemann Hypothesis.> > I think that follows quite easily from Schoenfeld's result> > of 1976, which is stated at Wikipedia's article on RH:> > > > http://en.wikipedia.org/wiki/Riemann_hypothesis> > > > P.S.  What is N_0 , 'N' being similar to '|N'   ?N_O are the positive integers without zero, i.e. zero is included in the set of natural numbers, so if you want to exclude zero you write N_0