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




Re: equivalence of truth of Riemann hypothesis
Posted:
Jan 5, 2013 2:41 PM


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: >> >>> $\exists C: \forall x \in \mathbb{N}_0: \left\pi(x)\operatorname{li}(x)\right \leq C \sqrt{x} \log(x)$ >> >>> >> >>> 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 >> > 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' ?



