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Re: equivalence of truth of Riemann hypothesis
Posted:
Jan 6, 2013 11:28 AM
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On Sat, 5 Jan 2013 12:44:58 -0800 (PST), Jean Dupont
<jeandupont115@gmail.com> wrote:
>Op zaterdag 5 januari 2013 18:51:24 UTC+1 schreef David C. Ullrich het volgende:
>> On Sat, 5 Jan 2013 08:30:50 -0800 (PST), Jean Dupont
>>
>> <jeandupont115@gmail.com> 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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>> >>
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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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>> >>
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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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>> >> >
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>> >>
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>> >> > Is this correct?
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>> >>
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>> >> >
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>> >>
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>> >> > thanks
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>> >>
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>> >> > jean
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>> >>
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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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>> >>
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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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>> >>
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>> >> head-way on the Riemann Hypothesis ...
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>> >>
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>> >>
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>> >> David Bernier
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>> >>
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>> >>
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>> >>
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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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>>
>>
>> When in Rome... If someone's going to read the TeX you posted, the
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>> fact that it's TeX instead of text just makes it harder to read. You
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>> shouldn't expect people to take the trouble to render your posts
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>> just so they can have the privilege of answering your question!
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>> Instead just post text:
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>>
>>
>> |pi(x) - li(x)| <= C sqrt(x)/log(x) .
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>>
>>
>> Simple. Perfectly clear.
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>>
>>
>I think the part \exists C: \forall x \in \mathbb{N}_0:
>should not be omitted...
Do you also think that this has any relevance to the point
I was making, about etiquette?
(Do you think that \mathbb{N}_0 is easier to
read than N_0 ?)
>
>regards,
>jean
>
>> >>
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>> >jean
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>> >>
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>> >>
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>> >> But, please see "error term" in Prime Number Theorem, here:
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>> >>
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>> >> primepages, 1901 von Koch result:
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>> >>
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>> >>
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>> >> < http://primes.utm.edu/notes/rh.html >
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>> >>
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>> >>
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>> >> I trust PrimePages. Also, Schoenfeld(1976) explicit bound:
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>> >>
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>> >> < http://en.wikipedia.org/wiki/Riemann_hypothesis > .
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