35 citations · 250 across the 28 of their papers we have counts for
8 papers · 1 filter
Modular Forms on the Double Half-Plane
John F. R. Duncan, David A. McGady
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provi…
Weight One Jacobi Forms and Umbral Moonshine
Miranda C. N. Cheng, John F. R. Duncan, Jeffrey A. Harvey
We analyze holomorphic Jacobi forms of weight one with level. One such form plays an important role in umbral moonshine, leading to simplifications of the statements of the umbral…
O'Nan moonshine and arithmetic
John F. R. Duncan, Michael H. Mertens, Ken Ono
Answering a question posed by Conway and Norton in their seminal 1979 paper on moonshine, we prove the existence of a graded infinite-dimensional module for the sporadic simple gro…
Optimal Mock Jacobi Theta Functions
Miranda C. N. Cheng, John F. R. Duncan
We classify the optimal mock Jacobi forms of weight one with rational coefficients. The space they span is thirty-four-dimensional, and admits a distinguished basis parameterized b…
The Jack Daniels Problem
John F. R. Duncan, Ken Ono
In 1975 Ogg offered a bottle of Jack Daniels for an explanation of the fact that the prime divisors of the order of the monster are the primes p for which the characteristic p supe…
Maass-Jacobi Poincaré series and Mathieu Moonshine
Kathrin Bringmann, John Duncan, Larry Rolen
Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to each conjugacy class of the largest sporadic simple group of Mathieu. We introduce a modification of t…
On the Discrete Groups of Mathieu Moonshine
Miranda C. N. Cheng, John F. R. Duncan
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 la…
Rademacher Sums and Rademacher Series
Miranda C. N. Cheng, John F. R. Duncan
We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe…