Publications (11)
Developing an OpenAI Gym-compatible framework and simulation environment for testing Deep Reinforcement Learning agents solving the Ambulance Location Problem
Michael Allen, Kerry Pearn, Tom Monks
Background and motivation: Deep Reinforcement Learning (Deep RL) is a rapidly developing field. Historically most application has been made to games (such as chess, Atari games, an…
Atkin and Swinnerton-Dyer congruences for meromorphic modular forms
Michael Allen, Ling Long, Hasan Saad
In the 1970's, Atkin and Swinnerton-Dyer conjectured that Fourier coefficients of holomorphic modular cusp forms on noncongruence subgroups of satisfy cer…
The Explicit Hypergeometric-Modularity Method II
Michael Allen, Brian Grove, Ling Long +1
In the first paper of this sequence, we provided an explicit hypergeometric modularity method by combining different techniques from the classical, -adic, and finite field setti…
Holomorphic projection for sesquiharmonic Maass forms
Michael Allen, Olivia Beckwith, Vaishavi Sharma
We study the holomorphic projection of mixed mock modular forms involving sesquiharmonic Maass forms. As a special case, we numerically express the holomorphic projection of a func…
On Some Hypergeometric Supercongruence Conjectures of Long
Michael Allen
In 2003, Rodriguez Villegas conjectured 14 supercongruences between hypergeometric functions arising as periods of certain families of rigid Calabi-Yau threefolds and the Fourier c…
Existence of -Quotients For Squarefree Levels
Michael Allen
In this paper, we investigate which modular form spaces can contain -quotients, functions of the form . For even and cop…