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Re: equivalence of truth of Riemann hypothesis
Posted:
Jan 5, 2013 3:44 PM
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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
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> <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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> >> > Is this correct?
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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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> >> < 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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> >>
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> >> head-way on the Riemann Hypothesis ...
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> >>
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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...
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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> >> primepages, 1901 von Koch result:
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> >> < http://primes.utm.edu/notes/rh.html >
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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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