- --- On Sun, 1/2/11, Andrey Kulsha wrote:
> There are also two new (very similar, huh)

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

> papers analyzing and improving these results:

> http://eprints.ma.man.ac.uk/1541/01/Munibah2010.pdf

Ewww...

Phil - --- On Sun, 1/2/11, Phil Carmody wrote:
> --- On Sun, 1/2/11, Andrey Kulsha wrote:

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

> > 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...

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 > It gets worse. Looking at the start of Chapter 3, Numerical Results (i),

I guess they mean the conjugated pair of zeta zeros.

> we have the assertion:

>

> Now we know that (gonna simplify glyphs, sorry)

>

> e^(iwy) e^(iwy) e^(-iwy)

> ------- = ------- + --------

> p B + iy B - iy

Best regards,

Andrey- --- On Sun, 1/2/11, Andrey Kulsha wrote:
> > e^(iwy) e^(iwy) e^(-iwy)

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.

> > ------- = ------- + --------

> > p B + iy B - iy

>

> I guess they mean the conjugated pair of zeta zeros.

Phil - _
> 3d. Re: Demichel

Shows that that dissertation did not have careful proofreading.

> 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

>

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