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

 Messages: [ Previous | Next ]
 David Bernier Posts: 3,662 Registered: 12/13/04
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:
>>
>>
>>
>>
>>
>>
>> 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' ?

Date Subject Author
1/5/13 David Bernier
1/5/13 Jean Dupont
1/5/13 David C. Ullrich
1/5/13 Jean Dupont
1/6/13 David C. Ullrich
1/5/13 David Bernier
1/5/13 Jean Dupont
1/7/13 AP
3/1/14 Brian Q. Hutchings
1/20/13 Luis A. Rodriguez
1/20/13 Luis A. Rodriguez
2/28/14 kraflyn@gmail.com
3/1/14 Christopher J. Henrich