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  1. ; ; ; (, Proceedings of the American Mathematical Society)
    Using predictions in mirror symmetry, Căldăraru, He, and Huang recently formulated a “Moonshine Conjecture at Landau-Ginzburg points” [arXiv:2107.12405, 2021] for Klein’s modular j j -function at j = 0 j=0 and j = 1728. j=1728. The conjecture asserts that the j j -function, when specialized at specific flat coordinates on the moduli spaces of versal deformations of the corresponding CM elliptic curves, yields simple rational functions. We prove this conjecture, and show that these rational functions arise from classical 2 F 1 _2F_1 -hypergeometric inversion formulae for the j j -function. 
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