[seqfan] Re: Where should I submit this?

[Charles Greathouse]

Wikipedia is not intended as a place for original research. If you want it
to show up there you would need to publish it first in a peer-reviewed
journal.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Tue, Apr 15, 2014 at 10:50 AM, Alonso Del Arte
<alonso.delarte at gmail.com>wrote:

> Have you thought about ProofWiki, PlanetMath or ArXiV? If your math and
> your TeX check out, those three should be very supportive. Your OEIS Wiki
> page might be a good place to sketch things out if your TeX skills need
> polishing.
>
> Getting true stuff into Wikipedia is too complicated. You'd have better
> luck with a hoax.
>
> Al
>
>
> On Sun, Apr 13, 2014 at 11:21 AM, Mats Granvik <matsgranvik at outlook.com
> >wrote:
>
> >
> >
> >
> > Two well known arithmetics functions, the von Mangoldt function and
> > the Möbius function, are found in this matrix "T" whose entries are the
> > Dirichlet
> > inverse of the Euler totient as follows:
> >
> > T(n,k) = a(GCD(n,k))
> >
> > where "n" is row index and "k" is column index.
> >
> > GCD stands for Greatest Common Divisor, and
> > "a" is the said Dirichlet inverse of the Euler totient function.
> >
> > starting:
> >
> > a(n) = 1, -1, -2, -1, -4, 2, -6, -1, -2, 4, -10, 2, -12, 6, 8
> >
> > "n" = 1,2,3,4,...
> >
> > T(n,k) is already entered as http://oeis.org/A023900 in the oeis.
> >
> > I had entered this into wikipedia with a link my math stackexchange
> > question
> > answered by "joriki" and another link to the OEIS page above.
> >
> > However today I found out I had been deleted from Wikipedia by some
> > user there.
> >
> > The claims of which one I believe is known by the result of Wolfgang
> > Schramm
> > on GCD matrices and the so called "Fourier-GCD transform" are:
> >
> > Claim 1 (Wolfgang Schramm):
> >
> > Sum_{k=1}^{k=n} T(n,k)*Cos(-2*Pi*k/n)/n = MobiusMu(n)
> >
> > Claim 2 (Mats Granvik, but probably known):
> >
> > Sum_{n=1}^{n=Infinity} = T(n,k)/n = MangoldtLambda(n)
> >
> > which by symmetry of matrix "T" allows for permutation of variables, of
> > course.
> >
> > I think these are important.
> >
> > Also at least a heuristic proof of the prime number theorem is given by
> > showing
> > that the von Mangoldt function is on average equal to 1.
> >
> > What has not been investigated are the sums in the other direction of the
> > "Fourier-GCD transform" matrix. They appear to converge to something
> > and the sequence is very irregular. The first convergent is found here:
> >
> > http://oeis.org/A210617
> >
> > 0.4790882572765523426...
> >
> >
> > Where should I submit these two claims? I would like to have it entered
> > into
> > Wikipedia. Two persons have said that for a proof of Claim 2, the von
> > Mangoldt
> > function series, Abels theorem is required, but GH from MO at Math
> Overflow
> > gave a simpler proof.
> >
> > Best regards,
> > Mats
> >
> >
> >
> > _______________________________________________
> >
> > Seqfan Mailing list - http://list.seqfan.eu/
> >
>
>
>
> --
> Alonso del Arte
> Author at SmashWords.com<
> https://www.smashwords.com/profile/view/AlonsoDelarte>
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
>
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