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

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David C. Ullrich

Posts: 21,553
Registered: 12/6/04
Re: equivalence of truth of Riemann hypothesis
Posted: Jan 6, 2013 11:28 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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
>>
>> >>
>>
>> >> 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
>>
>>
>>
>> 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 > .




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