Abstract
In this paper we prove the existence of an infinite dimensional graded super-module for the finite sporadic Thompson group $Th$ whose McKay-Thompson series are weakly holomorphic modular forms of weight $\frac 12$ satisfying properties conjectured by Harvey and Rayhaun.
Highlights
Introduction and statement of resultsOne of the greatest accomplishments of twentieth-century mathematics was certainly the classification of finite simple groups
The study of the representation theory of one of these groups, the Monster group M, the largest of the 26 sporadic simple groups, revealed an intriguing connection to modular forms: McKay and Thompson [41] were the first to observe that the dimensions of irreducible representations of the Monster group are closely related to Klein’s modular invariant
Rademacher series with a slightly different multiplier system mutatis mutandis, we find that the Rademacher sums we are interested in converge, assuming the convergence at s
Summary
Introduction and statement of resultsOne of the greatest accomplishments of twentieth-century mathematics was certainly the classification of finite simple groups. Definition 2.2 We call a smooth function f : H → C a harmonic (weak)1 Maaß form of weight k with multiplier system ψ, if the following conditions are satisfied: (1) We have f |k γ (τ ) = ψ(γ )f (τ ) for all γ ∈ Γ0(N ) and τ ∈ H, where we define
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