MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

3 added 7 characters in body

I am interested in pursuing an understanding of K-theory. Primarily, the $K_3(\mathbb{Z})$ algebraic K-group over ring of integers of an algebraic number field and its relationship to the $\mathbb{Z}/48$ ring of integers modulo 48.

This is (of course), again, from Terry Gannon's "Moonshine Beyond the Monster" where he talks about many amazing coincidences with the number 24, the Riemann Zeta Function $\Sigma_{n=1}^\infty (1/n)^{-1} = -1/12$, Apery's constant, where $\Sigma_{n=1}^\infty (1/n)^2 = \pi/6$ (which he states are both synonomous in their relationship to $K_3(\mathbb{Z})\leftrightarrow \mathbb{Z}/48$....)

A little harder to discern is the (possible) relationship of the Bimonster, $M (M \times M.x ) \rtimes \mathbb{Z}/2 \to M \wr 2$, and the Incidence Graph of the M-13 pseudogroup with 13 points and lines, (the 13 point, 13 line projective plane, where here, the coincidence would appear to be the number 26, which is the dimension of Bosonic String Theory (2 + 24 dimensions, the quantum harmonic oscillator on a 2-dimbrane, which relates to -1/12 above per John Baez "My Favorite Number is 24")). It's tempting to see the resemblance of 24 relating to the Monster, and 48 to the BiMonster, but that seems to obvious. Finally, is there any relevance in bringing in the M12-Mathieu group here, being so close to the M13-pseudogroup? I apologize ahead of time if this last paragraph is "shooting the moon" but hopefully my first two paragraphs are well-stated questions.

2 latex-ed the question up; added 1 characters in body

I am interested in pursuing an understanding of K-theory. Primarily, the K3(Z) $K_3(\mathbb{Z})$ algebraic K-group over ring of integers of an algebraic number field and its relationship to the Z/48 $\mathbb{Z}/48$ ring of integers modulo 48.

This is (of course), again, from Terry Gannon's "Moonshine Beyond the Monster" where he talks about many amazing coincidences with the number 24, the Riemann Zeta Function Sigma_1_oo $\Sigma_{n=1}^\infty (1/n)^-1 1/n)^{-1} = -1/12, 1/12$, Apery's constant, where Sigma_1_oo $\Sigma_{n=1}^\infty (1/n)^2 = pi/6 \pi/6$ (which he states are both synonomous in their relationship to K3(Z)<-> Z/48....)$K_3(\mathbb{Z})\leftrightarrow \mathbb{Z}/48$....)

A little harder to discern is the (possible) relationship of the Bimonster, $M X \times M .x Z/2 -> \mathbb{Z}/2 \to M wreath 2\wr 2$, and the Incidence Graph of the M-13 pseudogroup with 13 points and lines, (the 13 point, 13 line projective plane, where here, the coincidence would appear to be the number 26, which is the dimension of Bosonic String Theory (2 + 24 dimensions, the quantum harmonic oscillator on a 2-dimbrane, which relates to -1/12 above per John Baez "My Favorite Number is 24")). It's tempting to see the resemblance of 24 relating to the Monster, and 48 to the BiMonster, but that seems to obvious. Finally, is there any relevance in bringing in the M12-Mathieu group here, being so close to the M13-pseudogroup? I apologize ahead of time if this last paragraph is "shooting the moon" but hopefully my first two paragraphs are well-stated questions.

1

# Z/48 and Moonshine Beyond the Monster

I am interested in pursuing an understanding of K-theory. Primarily, the K3(Z) algebraic K-group over ring of integers of an algebraic number field and its relationship to the Z/48 ring of integers modulo 48.

This is (of course), again, from Terry Gannon's "Moonshine Beyond the Monster" where he talks about many amazing coincidences with the number 24, the Riemann Zeta Function Sigma_1_oo (1/n)^-1 = -1/12, Apery's constant, where Sigma_1_oo (1/n)^2 = pi/6 (which he states are both synonomous in their relationship to K3(Z)<-> Z/48....)

A little harder to discern is the (possible) relationship of the Bimonster, M X M .x Z/2 -> M wreath 2, and the Incidence Graph of the M-13 pseudogroup with 13 points and lines, (the 13 point, 13 line projective plane, where here, the coincidence would appear to be the number 26, which is the dimension of Bosonic String Theory (2 + 24 dimensions, the quantum harmonic oscillator on a 2-dimbrane, which relates to -1/12 above per John Baez "My Favorite Number is 24")). It's tempting to see the resemblance of 24 relating to the Monster, and 48 to the BiMonster, but that seems to obvious. Finally, is there any relevance in bringing in the M12-Mathieu group here, being so close to the M13-pseudogroup? I apologize ahead of time if this last paragraph is "shooting the moon" but hopefully my first two paragraphs are well-stated questions.