Michael Allen

collaborators

4 papers

math.NT2022

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…

math.NT2019

Existence of $η$ -Quotients For Squarefree Levels

Michael Allen

In this paper, we investigate which modular form spaces can contain $η$ -quotients, functions of the form $f (τ) = \prod_{δ ∣ N} η (δ τ)^{r_{δ}}$ . For $k \geq 2$ even and $N$ coprime to…

math.CO2019

A new combinatorial interpretation of the Fibonacci numbers squared

Kenneth Edwards, Michael A. Allen

We consider the tiling of an $n$ -board (a $1 \times n$ array of square cells of unit width) with half-squares ( $\frac{1}{2} \times 1$ tiles) and $(\frac{1}{2}, \frac{1}{2})$ -fence tiles. A $(\frac…

math.NT2019

Eta-quotients of Prime or Semiprime Level and Elliptic Curves

Michael Allen, Nicholas Anderson, Asimina Hamakiotes +2

From the Modularity Theorem proven by Wiles, Taylor, et al, we know that all elliptic curves are modular. It has been shown by Martin and Ono exactly which are represented by eta-q…

On Some Hypergeometric Supercongruence Conjectures of Long

Existence of η-Quotients For Squarefree Levels

A new combinatorial interpretation of the Fibonacci numbers squared

Eta-quotients of Prime or Semiprime Level and Elliptic Curves

Existence of $η$ -Quotients For Squarefree Levels