On the Discrete Groups of Mathieu MoonshineReport as inadecuate



 On the Discrete Groups of Mathieu Moonshine


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We prove that a certain space of cusp forms for the Hecke congruence group of a given level is one-dimensional if and only if that level is the order of an element of the second largest Mathieu group. As such, our result furnishes a direct analogue of Oggs observation that the normaliser of a Hecke congruence group of prime level has genus zero if and only if that prime divides the order of the Fischer-Griess monster group. The significance of the cusp forms under consideration is explained by the Rademacher sum construction of the McKay-Thompson series of Mathieu moonshine. Our result supports a conjectural characterisation of the discrete groups and multiplier systems arising in Mathieu moonshine.



Author: Miranda C. N. Cheng; John F. R. Duncan

Source: https://archive.org/



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