Non-moonshine-likeness conjecture for the completely replicable function 9a

Let

f9a=q1+14q2+65q5+156q8+f_{9a}=q^{-1}+14q^2+65q^5+156q^8+\cdots

be the indicated completely replicable function. Non-moonshine-likeness conjecture for f9af_{9a}. The function f9af_{9a} is non-moonshine-like. Establishing this would remove the remaining possible primitive exception in the paper's characterization of moonshine-like functions. The paper proves that all primitive non-monstrous functions except possibly 9a9a are non-moonshine-like, and that all non-monstrous functions except possibly 9a9a, 63a63a, and 117a117a are non-moonshine-like.

Sources & referencesView supporting material

Primary source

Scott Carnahan, Takahiro Komuro and Satoru Urano, “Characterizing Moonshine Functions by Vertex-Operator-Algebraic Conditions”, arXiv:1712.10160 (2018).

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