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

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David Bernier

Posts: 3,276
Registered: 12/13/04
Re: equivalence of truth of Riemann hypothesis
Posted: Jan 5, 2013 11:06 AM
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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 ...

But, please see "error term" in Prime Number Theorem, here:

primepages, 1901 von Koch result:

< http://primes.utm.edu/notes/rh.html >

I trust PrimePages. Also, Schoenfeld(1976) explicit bound:

< http://en.wikipedia.org/wiki/Riemann_hypothesis > .






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