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:

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> > 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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> >>> 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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> >>> Is this correct?

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> >>> thanks

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> >>> jean

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> >> The movie "A Beautiful Mind" about John Nash is now on Youtube:

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> >> < http://www.youtube.com/watch?v=OOWT1371DRg> .

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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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> > 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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> > 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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> > 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