172 citations · 846 across the 36 of their papers we have counts for
9 papers · 1 filter
Class Numbers, Congruent Numbers and Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Michael H. Mertens
In earlier work we initiated a program to study relationships between finite groups and arithmetic geometric invariants of modular curves in a systematic way. In the present work w…
Class Numbers, Cyclic Simple Groups and Arithmetic
Miranda C. N. Cheng, John F. R. Duncan, Michael H. Mertens
Here we initiate a program to study relationships between finite groups and arithmetic-geometric invariants in a systematic way. To do this we first introduce a notion of optimal m…
Cone Vertex Algebras, Mock Theta Functions, and Umbral Moonshine Modules
Miranda C. N. Cheng, Gabriele Sgroi
We describe a family of indefinite theta functions of signature that can be expressed in terms of trace functions of vertex algebras built from cones in lattices. The famil…
Meromorphic Jacobi Forms of Half-Integral Index and Umbral Moonshine Modules
Miranda C. N. Cheng, John F. R. Duncan
In this work we consider an association of meromorphic Jacobi forms of half-integral index to the pure D-type cases of umbral moonshine, and solve the module problem for four of th…
Generalised Umbral Moonshine
Miranda C. N. Cheng, Paul de Lange, Daniel P. Z. Whalen
Umbral moonshine describes an unexpected relation between 23 finite groups arising from lattice symmetries and special mock modular forms. It includes the Mathieu moonshine as a sp…
Umbral Moonshine and the Niemeier Lattices
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey
In this paper we relate umbral moonshine to the Niemeier lattices: the 23 even unimodular positive-definite lattices of rank 24 with non-trivial root systems. To each Niemeier latt…
Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey
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…
The Largest Mathieu Group and (Mock) Automorphic Forms
Miranda C. N. Cheng, John F. R. Duncan
We review the relationship between the largest Mathieu group and various modular objects, including recent progress on the relation to mock modular forms. We also review the connec…
On Rademacher Sums, the Largest Mathieu Group, and the Holographic Modularity of Moonshine
Miranda C. N. Cheng, John F. R. Duncan
Recently a conjecture has been proposed which attaches (mock) modular forms to the largest Mathieu group. This may be compared to monstrous moonshine, in which modular functions ar…