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Re: equivalence of truth of Riemann hypothesis
Posted:
Jan 5, 2013 2:41 PM
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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:
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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
>>
>>
>>
>> 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
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>> head-way on the Riemann Hypothesis ...
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>>
>> David Bernier
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>>
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>> 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' ?
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