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Monstrous moonshine. (English) Zbl 0424.20010


MSC:

20D05 Finite simple groups and their classification
20D08 Simple groups: sporadic groups
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Online Encyclopedia of Integer Sequences:

Coefficients of modular function j as power series in q = e^(2 Pi i t). Another name is the elliptic modular invariant J(tau).
Degrees of irreducible representations of Monster group M.
The 15 supersingular primes: primes dividing order of Monster simple group.
McKay-Thompson series of class 11A for the Monster group with a(0) = -5.
McKay-Thompson series of class 2B for the Monster group with a(0) = -24.
McKay-Thompson series of class 1A for the Monster group with a(0) = 24.
McKay-Thompson series of class 2A for the Monster group with a(0) = 24.
McKay-Thompson series of class 2a for the Monster group.
McKay-Thompson series of class 3A for the Monster group with a(0) = 0.
McKay-Thompson series of class 3B for the Monster group.
McKay-Thompson series of class 3C for the Monster group.
McKay-Thompson series of class 2B for the Monster group.
McKay-Thompson series of class 4B for the Monster group.
McKay-Thompson series of class 4C for the Monster group.
McKay-Thompson series of class 4D for the Monster group.
McKay-Thompson series of class 4a for the Monster group.
McKay-Thompson series of class 5A for the Monster group.
McKay-Thompson series of class 5B for the Monster group with a(0) = 0.
McKay-Thompson series of class 5a for Monster.
McKay-Thompson series of class 6A for Monster.
McKay-Thompson series of class 6B for Monster.
McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
McKay-Thompson series of class 6D for Monster.
McKay-Thompson series of class 6E for Monster (and, apart from signs, of class 12B).
Expansion of Product_{m>=1} (1 + q^m)^(-8).
McKay-Thompson series of class 6a for Monster.
McKay-Thompson series of class 6b for the Monster group.
McKay-Thompson series of class 6c for Monster.
Coefficients of completely replicable function ”6d”.
McKay-Thompson series of class 7A for Monster.
McKay-Thompson series of class 8A for Monster.
McKay-Thompson series of class 9A for Monster.
Expansion of 16 * (1 + k^2)^4 /(k * k’^2)^2 in powers of q where k is the Jacobian elliptic modulus, k’ the complementary modulus and q is the nome.
Coefficients of the modular function J = j - 744.
Multiplicity of trivial character in V_n, where V = Sum V_n is the graded module for the Monster simple group.
Expansion of Product_{m>=1} (1+q^m)^(-4).
Expansion of Product_{m>=1} (1+q^m)^(-6).
McKay-Thompson series of class 8E for the Monster group.
Expansion of 16/lambda(z) in powers of nome q = exp(Pi*i*z).
Expansion of (eta(q) / eta(q^7))^4 in powers of q.
McKay-Thompson series of class 3B for the Monster group with a(0) = -12.
McKay-Thompson series of class 7A for the Monster group with a(0) = 10.
McKay-Thompson series of class 3A for the Monster group with a(0) = 42.
McKay-Thompson series of class 13A for the Monster group with a(0) = -2.
McKay-Thompson series of class 13A for the Monster group with a(0) = 0.
McKay-Thompson series of class 71A for Monster.
McKay-Thompson series of class 2B for the Monster group with a(0) = 40.
McKay-Thompson series of class 2A for Monster.
McKay-Thompson series of class 2B for the Monster group with a(0) = -8.
McKay-Thompson series of class 3A for Monster. Expansion of Hauptmodul for X_0^{+}(3).
McKay-Thompson series of class 3B for the Monster group with a(0) = -3.
McKay-Thompson series of class 5A for Monster.
McKay-Thompson series of class 5B for the Monster group with a(0) = 1.
McKay-Thompson series of class 6A for Monster.
McKay-Thompson series of class 6B for Monster with a(0) = 7.
McKay-Thompson series of class 6C for Monster (and, apart from signs, of class 12A).
McKay-Thompson series of class 6D for Monster with a(0) = 1.
McKay-Thompson series of class 6E for the Monster group with a(0) = 1.
McKay-Thompson series of class 7A for the Monster group with a(0) = 3.
McKay-Thompson series of class 8A for Monster.
McKay-Thompson series of class 9A for the Monster group with a(0) = 3.
McKay-Thompson series of class 7B for the Monster group.
McKay-Thompson series of class 8C for Monster.
Multiplicity of irreducible character IRR2 of Monster simple group in n-th head character.
Table giving multiplicity of k-th irreducible character of Monster simple group in n-th head character, read by antidiagonals.
McKay-Thompson series of class 15D for the Monster group.
Expansion of f(x, x) * f(x, -x^2) in powers of x where f(,) is a Ramanujan theta function.
Products of exactly two supersingular primes (A002267).
McKay-Thompson series of class 57A for the Monster group.
Coefficients of replicable function number 49a with a(0) = 3.
McKay-Thompson series of class 29A for the Monster group with a(0) = 2.
McKay-Thompson series of class 24I for the Monster group with a(0) = 2.
1,0,1 followed by 0,0,0,...
Divisors of 196560.
Products of supersingular primes (A002267).
Partial sums of dimensions of irreducible representations of Monster group M.
Divisors of 196883.