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Topic: equivalence of truth of Riemann hypothesis
Replies: 13   Last Post: Mar 1, 2014 11:10 AM

 Messages: [ Previous | Next ]
 Jean Dupont Posts: 7 Registered: 1/5/12
Re: equivalence of truth of Riemann hypothesis
Posted: Jan 5, 2013 11:30 AM

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?
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> >
>
> > thanks
>
> > jean
>
>
>
> The movie "A Beautiful Mind" about John Nash is now on Youtube:
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>
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> < http://www.youtube.com/watch?v=OOWT1371DRg > .
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>
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> I think John Nash in the movie or in reality tried to make
>
> head-way on the Riemann Hypothesis ...
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>
>
> 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
>
>
> But, please see "error term" in Prime Number Theorem, here:
>
>
>
> primepages, 1901 von Koch result:
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>
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> < http://primes.utm.edu/notes/rh.html >
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>
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> I trust PrimePages. Also, Schoenfeld(1976) explicit bound:
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>
>
> < http://en.wikipedia.org/wiki/Riemann_hypothesis > .

Date Subject Author
1/5/13 David Bernier
1/5/13 Jean Dupont
1/5/13 David C. Ullrich
1/5/13 Jean Dupont
1/6/13 David C. Ullrich
1/5/13 David Bernier
1/5/13 Jean Dupont
1/7/13 AP
3/1/14 Brian Q. Hutchings
1/20/13 Luis A. Rodriguez
1/20/13 Luis A. Rodriguez
2/28/14 kraflyn@gmail.com
3/1/14 Christopher J. Henrich