Re: Riemann Hypothesis


"OwlHoot" <ravensdean@xxxxxxxxxxxxxx> wrote in message
news:1177639648.621710.153350@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
On Apr 26, 6:48 pm, "Geert-Jan Uytdewilligen"
<g.a.uytdewilli...@xxxxxxxxx> wrote:
<toni.lass...@xxxxxxxxx> wrote in message

news:1177607036.003745.50230@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> On 25
huhti, 18:56, "Geert-Jan Uytdewilligen"
<g.a.uytdewilli...@xxxxxxxxx> wrote:
I would like to hear your comments on my proof (i hope) of the
Riemann
Hypothesis (RH)

How do you know that the series expansion of xi around z=1/2 has
exactly the same zeros as xi?

IF the radius of convergence is infinity, then Xi is identical to its
series
expansion. Xi is analytic at all finite points of the complex plane,
so it agrees with its Taylor series. Taylor's theorem: A series
representation is valid in the largest open disk with center 1/2
contained in D, > if f(z) is analytic in D.

I seem to recall reading that the Riemann zeta function has an
essential singularity at infinity.

Of course. A bounded entire function is a constant.(Liouville) But as i
said,
at all finite points it is analytic.

Is your switching of the order of
summation and integration etc valid when that is taken into
account?

The sum must be uniform convergent. The fact that the sum is calculated
is proof that it converges uniform to that sum. If you disagree, and think
i should prove it before taking the sum, please let me know.


Why not try emailing it to de Branges, the guy who proved the
Bieberbach conjecture and I gather has been trying for some
years to prove RH?

Mr de Branges? I'll look for him on the internet.

If there is a flaw (and, no disrespect, but this seems distinctly
likely given the number of expert analysts over the years
who have tried and failed to prove it) he'd likely spot it.

Thank you.

Cheers

John R Ramsden



.

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