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