Formal Versions of Conway's and Norton's Conjectures
The first conjecture made by Conway and Norton was the so-called "moonshine conjecture"; it states that there is an infinite-dimensional graded M-module
with for all m, where
From this it follows that every element g of M acts on each Vm and has character value
which can be used to construct the McKay–Thompson series of g:
The second conjecture of Conway and Norton then states that with V as above, for every element g of M, there is a genus zero subgroup K of PSL2(R), commensurable with the modular group Γ = PSL2(Z), such that is the normalized main modular function for K.
Read more about this topic: Monstrous Moonshine
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