Umbral Moonshine

@inproceedings{Cheng2012UmbralM,
  title={Umbral Moonshine},
  author={Miranda C. N. Cheng and J. Duncan and J. Harvey},
  year={2012}
}
We describe surprising relationships between automorphic forms of various kinds, imaginary quadratic number fields and a certain system of six finite groups that are parameterised naturally by the divisors of twelve. The Mathieu group correspondence recently discovered by Eguchi–Ooguri–Tachikawa is recovered as a special case. We introduce a notion of extremal Jacobi form and prove that it characterises the Jacobi forms arising by establishing a connection to critical values of Dirichlet series… Expand
114 Citations
Generalised Umbral Moonshine
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Umbral moonshine and the Niemeier lattices
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K3 Elliptic Genus and an Umbral Moonshine Module
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Equivariant K3 Invariants
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Much ado about Mathieu
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On Divisors, Congruences, and Symmetric Powers of Modular Forms
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Umbral Moonshine and K3 Surfaces
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THE MOONSHINE MODULE FOR CONWAY’S GROUP
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Derived equivalences of K3 surfaces and twined elliptic genera
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