Conway, J. H.; Norton, S. P. Monstrous moonshine. (English) Zbl 0424.20010 Bull. Lond. Math. Soc. 11, 308-339 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 49 ReviewsCited in 276 Documents MSC: 20D05 Finite simple groups and their classification 20D08 Simple groups: sporadic groups Keywords:sporadic simple group; monster PDFBibTeX XMLCite \textit{J. H. Conway} and \textit{S. P. Norton}, Bull. Lond. Math. Soc. 11, 308--339 (1979; Zbl 0424.20010) Full Text: DOI 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.