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Re: equivalence of truth of Riemann hypothesis
Posted:
Jan 6, 2013 11:28 AM


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: >> >> >> >> >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: >> >> >> >> >> >> > $\exists C: \forall x \in \mathbb{N}_0: \left\pi(x)\operatorname{li}(x)\right \leq C \sqrt{x} \log(x)$ >> >> >> >> >> >> > >> >> >> >> >> >> > 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 >> >> >> >> >> >> headway on the Riemann Hypothesis ... >> >> >> >> >> >> >> >> >> >> >> >> David Bernier >> >> >> >> >> >> >> >> >> >> >> >> 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/educationaltools/latexrendererneditor.html >> >> >> >> When in Rome... If someone's going to read the TeX you posted, the >> >> fact that it's TeX instead of text just makes it harder to read. You >> >> shouldn't expect people to take the trouble to render your posts >> >> just so they can have the privilege of answering your question! >> >> Instead just post text: >> >> >> >> pi(x)  li(x) <= C sqrt(x)/log(x) . >> >> >> >> Simple. Perfectly clear. >> >> >> >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 > >> >> >> >> >jean >> >> >> >> >> >> >> >> >> 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 > .



