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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 3:36 PM

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:
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> >> On 01/05/2013 09:55 AM, Jean Dupont wrote:
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> >>
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> >>> In the book "Math goes to the movies" it is stated that the truth of the Riemann hypothesis is equivalent to the following statement:
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> >>> $\exists C: \forall x \in \mathbb{N}_0: \left|\pi(x)-\operatorname{li}(x)\right| \leq C \sqrt{x} \log(x)$
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> >>>
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> >>> Is this correct?
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> >>>
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> >>> thanks
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> >>> jean
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> >>
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> >>
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> >> The movie "A Beautiful Mind" about John Nash is now on Youtube:
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> >> I think John Nash in the movie or in reality tried to make
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> >> head-way on the Riemann Hypothesis ...
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> >> David Bernier
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> >> P.S. I'm afraid I can't read Tex or Latex ...
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> > just copy/paste the line
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> >
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> > exists C: \forall x \in \mathbb{N}_0: \left|\pi(x)-\operatorname{li}(x)\right| \leq C \sqrt{x} \log(x)
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> >
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> > in the box shown on the following web page and press render:
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> > http://itools.subhashbose.com/educational-tools/latex-renderer-n-editor.html
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> >>
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> > jean
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> Yes, I believe that is equivalent to the Riemann Hypothesis.
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> I think that follows quite easily from Schoenfeld's result
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> of 1976, which is stated at Wikipedia's article on RH:
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> http://en.wikipedia.org/wiki/Riemann_hypothesis
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> 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

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