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• ... In 1914, numerical evidence proved that π(x)
Message 1 of 8 , Jan 2, 2011
--- On Sun, 1/2/11, Andrey Kulsha wrote:
> There are also two new (very similar, huh)
> papers analyzing and improving these results:
> http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf

"In 1914, numerical evidence proved that π(x) < li(x) for all x. "

Ewww...

Phil
• ... It gets worse. Looking at the start of Chapter 3, Numerical Results (i), we have the assertion: Now we know that (gonna simplify glyphs, sorry) e^(iwy)
Message 2 of 8 , Jan 2, 2011
--- On Sun, 1/2/11, Phil Carmody wrote:
> --- On Sun, 1/2/11, Andrey Kulsha wrote:
> > There are also two new (very similar, huh)
> > papers analyzing and improving these results:
> > http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf
>
> "In 1914, numerical evidence proved that π(x) < li(x)
> for all x. "
>
> Ewww...

It gets worse. Looking at the start of Chapter 3, Numerical Results (i), we have the assertion:

Now we know that (gonna simplify glyphs, sorry)

e^(iwy) e^(iwy) e^(-iwy)
------- = ------- + --------
p B + iy B - iy

where none of the terms are defined. It seems chapter 2 most recently defined p = B + iy.

So his assertion seems to be that:

e^(iwy) e^(iwy) e^(-iwy)
------- = ------- + --------
B + iy B + iy B - iy

Or:

e^(-iwy)
0 = --------
B - iy

Or are my eyes playing tricks with me?

Phil
• ... I guess they mean the conjugated pair of zeta zeros. Best regards, Andrey
Message 3 of 8 , Jan 2, 2011
> It gets worse. Looking at the start of Chapter 3, Numerical Results (i),
> we have the assertion:
>
> Now we know that (gonna simplify glyphs, sorry)
>
> e^(iwy) e^(iwy) e^(-iwy)
> ------- = ------- + --------
> p B + iy B - iy

I guess they mean the conjugated pair of zeta zeros.

Best regards,

Andrey
• ... Maths by guesswork? What happened to rigour? Then again, seeing how long those two take to get from 24/8 to 3, I suspect that the papers will be closely
Message 4 of 8 , Jan 2, 2011
--- On Sun, 1/2/11, Andrey Kulsha wrote:
> > e^(iwy)    e^(iwy)   e^(-iwy)
> > ------- =  ------- + --------
> >    p        B + iy    B - iy
>
>     I guess they mean the conjugated pair of zeta zeros.

Maths by guesswork? What happened to rigour? Then again, seeing how long those two take to get from 24/8 to 3, I suspect that the papers will be closely associated with rigor mortis.

Phil
• _ ... Shows that that dissertation did not have careful proofreading. http://primes.utm.edu/howmany.shtml However in 1914 Littlewood proved that pi(x)-Li(x)
Message 5 of 8 , Jan 2, 2011
_
> 3d. Re: Demichel
> Posted by: "Phil Carmody" thefatphil@... thefatphil
> Date: Sun Jan 2, 2011 4:32 am ((PST))
>
> --- On Sun, 1/2/11, Andrey Kulsha wrote:
>> There are also two new (very similar, huh)
>> papers analyzing and improving these results:
>> http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf
>
> "In 1914, numerical evidence proved that π(x)< li(x) for all x. "
>
> Ewww...
>
> Phil
>

Shows that that dissertation did not have careful proofreading.

http://primes.utm.edu/howmany.shtml

However in 1914 Littlewood proved that pi(x)-Li(x) assumes both positive
and negative values infinitely often.

Kermit
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