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Re: equivalence of truth of Riemann hypothesis
Posted:
Jan 5, 2013 3:36 PM


Op zaterdag 5 januari 2013 20:41:23 UTC+1 schreef David Bernier het volgende: > 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' ?
N_O are the positive integers without zero, i.e. zero is included in the set of natural numbers, so if you want to exclude zero you write N_0



