Date: Jan 5, 2013 2:41 PM
Author: David Bernier
Subject: Re: equivalence of truth of Riemann hypothesis
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

>>

>> head-way 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/educational-tools/latex-renderer-n-editor.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' ?