Tuesday, 30 April 2013

Moonshine Monster Group & Fourier

Moonshine 196,883
What object can exist in 196,883 dimension ?

Simon Norton: "I can explain to you what Moonshine (Monster Group) is in one sentence.
"It is the voice of God."

While all the 5 mathematicians have been fully exhausted after 15 years of effort to categorize all Simple Groups in the Universe, only Simon Norton remains lonely in the search of the largest Monster Group (Moonshine).

Conway, who migrated from Cambridge to Princeton, does not want to touch anything on Group now, said, "Simon is the only person on earth who knows Moonshine".

Monster Group M, order |M|=
$latex 2^{46}. 3^{20}. 5^{9}. 11^{2}. 13^{3}. 17.19.23.29.31.41.47.59.71$

Moonshine Monster Group dimensions (dj) & relationship with Fourier expansion of coefficients (cj) in Modular Function:
$latex x^{-1} + 744+196,884x + 21,493,760 x^{2} + 864,229,970x^{3} +\dots $
$latex c_n= c_1+c_2+...c_{n-1} + d_{n}$
where
$latex d_1 = 196,883$
$latex d_2 = 21,296,876$
$latex d_3 = 842,609,326$
and
$latex c_1 = 1+ d_1 = 196,884$
$latex c_2 = c_1+d_2 = 21,493,760$
$latex c_3 = c_1 + c_2 + d_3 = 864,229,970$

What a coincidence! no wonder Conway said this discovery was the most exciting event in his life.

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