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I should rewrite the paper as you say. I sent it to a Journal a
few years ago, but I don’t think they understood it. After that I shelved
it until I saw the proposal Tim was making for this web site. I still believe
though it is correct because it is based on a simple idea, which is the kind of
proof people find satisfying. If the integers can occur randomly even in an
infinite sequence then anything that applies to random numbers also applies to
them. So to say the RH is true for N random numbers is the same thing as saying
it is true for 1 to N. Because the RH is already proven to be true for N
random numbers that is the basic proof.
So the integers in ascending order can either occur by selecting
numbers randomly or they cannot. If they can then there is no reason to exclude
them from the results for random numbers here, which have the required rate of
growth. I will try and read your paper and comment later. I know the Merten’s
Conjecture was proven false for the exponent ˝ but not for ˝ + e, does this
affect your proof?
From: UnsolvedProblems@yahoogroups.com
[mailto:UnsolvedProblems@yahoogroups.com] On Behalf Of Jeffrey Cook
Sent: Saturday, 2 June 2007 8:46 AM
To: UnsolvedProblems@yahoogroups.com
Subject: RE: [UnsolvedProblems] Jeff Cook's RH proof...
Greg,
I think your goal was the same as mine. But the
equivalence between the Mobius Function, then sum of which is called Mertens'
Function is shown mathematically in equation 3 of my paper. Proving that
M(k) is big oh of k^(1/2+e) would directly prove the RH. So I did in fact
do that. I think this is what you are speaking of in terms of equivalent
growth. But the depth of the Mobius function is described in depth in my
paper beginning on page 50. And I cover all the points which the articles
you provided are based on.
But there are many other things I see as weaknesses in your
paper from the very small to the very large...just for one
instance, proposition2. This is not a proposition at all. It
has already been proven a long while back. So its a proof. There
are an infinite number of primes...we know that. Such simple mistakes
detur readers who are seriously studying the RH in depth.
I would recommend to you and others seriously wanting to
understand the RH, study my proof and work out the equations with a calculator
in unison. Then you will see how the RH is true with simple evidence of
1+1=2, etc..
Jeff
Greg Orme <grego@...> wrote:
Hi Jeff,
If you read these it may help.
This path is quite different to the one you are following but it does not require using complex numbers. Note the attached part of this article, that proving the Mobius Function has the required rate of growth is equivalent to proving the Riemann Hypothesis.
Greg.
From: UnsolvedProblems@yahoogroups.com [mailto:UnsolvedProblems@yahoogroups.com] On Behalf Of Jeffrey Cook
Sent: Friday, 1 June 2007 7:46 AM
To: UnsolvedProblems@yahoogroups.com
Subject: RE: [UnsolvedProblems] Jeff Cook's RH proof...
Greg,
You provide the equivalence to the Mobius function's zeros, which have nothing to do with the Riemann Zeta Function non-trivial zeros. The RH suggests that all the non-trivial zeros of the Zeta Function have a real part 1/2. You are not dealing with the Riemann Zeta Function in your paper...just the Zeta Function for Real numbers strictly. There are no non-trivial zeros involving strictly Real numbers. They are all complex.
Perhaps I am missing something?
Jeff
Greg Orme <grego@...> wrote:My proof is about an equivalent formulation of the Riemann Hypothesis, but very different to yours.
From: UnsolvedProblems@yahoogroups.com [mailto:UnsolvedProblems@yahoogroups.com] On Behalf Of Jeffrey N Cook
Sent: Thursday, 31 May 2007 8:01 AM
To: UnsolvedProblems@yahoogroups.com
Subject: [UnsolvedProblems] Jeff Cook's RH proof...All,
I just thought I'd start a post to offer any explanations on my proof
which is currently being presented on the Unsolved Problems website.
There are a number of highly qualified mathematicians from around the
world with there hands on this paper. The comments I have received
were vari ed...
"Fascinating..."
to...
"...[does] not fit the standard framework of mathematics."
I would like to comment on the latter. The mathematics I present in
this paper are not extreme stretches from conventional wisdom. I
simply expanded on already known rules with new findings. There is
no break from standard mathematics.
What this paper does is deal with every known aspect of the Riemann
Hypothesis and covers each point carefully, though quickly. It may
be hard for most to follow everything...even the especially
mathematically inclined. However, I would be happy to explain each
equation and point to the paper with anyone and/or explain the
hypothesis to amateurs to make sure everyone is on the same page.
Please feel free to ask any questions openly in this forum. Please
do not email me directly, as others may want to hear the arguments.
BTW, the other proof on the website is completely lacking and deals
very little with the actual hypothesis. This is not to belittle the
author's work. It is just to make things completely clear what the
real issues with this problem indeed are and how I have discovered
quite new items.
Cheers,
Jeff Cook
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