Nathan C. Ryan
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View article: Explicit families of congruences for the overpartition function
Explicit families of congruences for the overpartition function Open
In this article we exhibit new explicit families of congruences for the overpartition function, making effective the existence results given previously by Treneer. We give infinite families of congruences modulo m for $$m = 3, 5, 7, 11$$ …
View article: Repulsion of zeros close to $s=1/2$ for L-functions
Repulsion of zeros close to $s=1/2$ for L-functions Open
In this paper we present results of several experiments in which we model the repulsion of low-lying zeros of L-functions using random matrix theory. Previous work has typically focused on the twists of L-functions associated to elliptic c…
View article: Explicit families of congruences for the overpartition function
Explicit families of congruences for the overpartition function Open
In this article we exhibit new explicit families of congruences for the overpartition function, making effective the existence results given previously by Treneer. We give infinite families of congruences modulo $m$ for $m = 5, 7, 11$, and…
View article: Efficient computation of the overpartition function and applications
Efficient computation of the overpartition function and applications Open
In this paper we develop a method to calculate the overpartition function efficiently using a Hardy-Rademacher-Ramanujan type formula, and we use this method to find many new Ramanujan-style congruences, whose existence is predicted by Tre…
View article: Vanishing of Quartic and Sextic Twists of $L$-functions
Vanishing of Quartic and Sextic Twists of $L$-functions Open
Let $E$ be an elliptic curve over $\mathbf{Q}$. We conjecture asymptotic estimates for the number of vanishings of $L(E,1,χ)$ as $χ$ varies over all primitive Dirichlet characters of orders 4 and 6, subject to a mild hypothesis on $E$. Our…
View article: Carceral algorithms and the history of control: An analysis of the Pennsylvania additive classification tool
Carceral algorithms and the history of control: An analysis of the Pennsylvania additive classification tool Open
Scholars have focused on algorithms used during sentencing, bail, and parole, but little work explores what we term “carceral algorithms” that are used during incarceration. This paper is focused on the Pennsylvania Additive Classification…
View article: Analysis of the Pennsylvania Additive Classification Tool: Biases and Important Features
Analysis of the Pennsylvania Additive Classification Tool: Biases and Important Features Open
The Pennsylvania Additive Classification Tool (PACT) is a carceral algorithm used by the Pennsylvania Department of Corrections in order to determine the security level for an incarcerated person in the state's prison system. For a newly i…
View article: Uncertainty in Criminal Justice Algorithms: simulation studies of the\n Pennsylvania Additive Classification Tool
Uncertainty in Criminal Justice Algorithms: simulation studies of the\n Pennsylvania Additive Classification Tool Open
Much attention has been paid to algorithms related to sentencing, the setting\nof bail, parole decisions and recidivism while less attention has been paid to\ncarceral algorithms, those algorithms used to determine an incarcerated\nindivid…
View article: Uncertainty in Criminal Justice Algorithms: simulation studies of the Pennsylvania Additive Classification Tool
Uncertainty in Criminal Justice Algorithms: simulation studies of the Pennsylvania Additive Classification Tool Open
Much attention has been paid to algorithms related to sentencing, the setting of bail, parole decisions and recidivism while less attention has been paid to carceral algorithms, those algorithms used to determine an incarcerated individual…
View article: KALMUS: tools for color analysis of films
KALMUS: tools for color analysis of films Open
KALMUS is a Python package for the computational analysis of colors in films.It provides quantitative tools to study and compare the use of film color.This package serves two purposes: (1) various ways to measure, calculate and compare a f…
View article: Congruences satisfied by eta-quotients
Congruences satisfied by eta-quotients Open
The values of the partition function, and more generally the Fourier coefficients of many modular forms, are known to satisfy certain congruences. Results given by Ahlgren and Ono for the partition function and by Treneer for more general …
View article: Analytic $L$-functions: Definitions, theorems, and connections
Analytic $L$-functions: Definitions, theorems, and connections Open
$L$-functions can be viewed axiomatically, such as in the formulation due to Selberg, or they can be seen as arising from cuspidal automorphic representations of $\textrm{GL}(n)$, as first described by Langlands. Conjecturally these two de…
View article: Analytic evaluation of Hecke eigenvalues for classical modular forms
Analytic evaluation of Hecke eigenvalues for classical modular forms Open
We propose a method for computing approximations to the Hecke eigenvalues of a classical modular eigenform $f$, based on the analytic evaluation of $f$ at points in the upper half plane. Our approach works with arbitrary precision, allows …
View article: A Network-Theoretic Analysis of Hospital Admission, Transfer, and Discharge Data.
A Network-Theoretic Analysis of Hospital Admission, Transfer, and Discharge Data. Open
Comprehending complex behavior of flow within a graph is of interest to clinicians and mathematicians alike. In this study we examine admission, discharge, and transfer data of patients within a hospital system, and process the importance …
View article: Formulas for central values of twisted spin $L$-functions attached to paramodular forms
Formulas for central values of twisted spin $L$-functions attached to paramodular forms Open
In the 1980s Böcherer formulated a conjecture relating the central values of the imaginary quadratic twists of the spin $L$-function attached to a Siegel modular form $F$ to the Fourier coefficients of $F$. This conjecture has been proved…