J. Cullinan

activity

20192026

most citedOn the arithmetic of Padé approximants to the exponential function

1 citations · 2 across the 10 of their papers we have counts for

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9 papers · 1 filter

math.NT2026

Hasse-Witt invariants for trace forms of Jacobi polynomials

John Cullinan, Farshid Hajir, Elisabeth Young

In \cite{feit}, Feit used the Generalized Laguerre Polynomials (GLP) to prove that the groups $A_{5}$ and $A_{7}$ occur as Galois groups over $\Q$. Hajir, i…

math.NT2026

Kodaira-Neron statistics for rational elliptic curves with $j$ -invariant 0 and 1728

John Cullinan, Sebastian Sargenti

Elliptic curves over $\Q$ with $j$ -invariant 0 or 1728 have additive reduction at all primes of bad reduction. In addition, all elliptic curves with $j$ -invariant 0 have bad reduct…

math.NT2023

The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I

John Cullinan, Nathan Kaplan

Let $ℓ$ be a prime number and let $E$ and $E^{'}$ be $ℓ$ -isogenous elliptic curves defined over a finite field $k$ of characteristic $p \neq = ℓ$ . Suppose the groups $E (k)$ and…

math.NT2022

On the Irreducibility of the Krawtchouck Polynomials

John Cullinan

The Krawtchouck polynomials arise naturally in both coding theory and probability theory and have been studied extensively from these points of view. However, very little is known…

math.NT2021

Realizations of Unisingular Representations by Hyperelliptic Jacobians

John Cullinan

A representation of a finite group $G$ on a finite dimensional vector space $V$ is called \textbf{unisingular} if every $g \in G$ has 1 as an eigenvalue in its action on $V$ . In thi…

math.NT2020

Unisingular representations in arithmetic and Lie theory

John Cullinan, Alexandre Zalesski

Let G be a subgroup of GL(V), where V is a finite dimensional vector space over a finite field of characteristic p >0. If det(g-1) = 0 for all g \in G then we call G a fixed-point…

math.NT2020★ 1 cited

On the arithmetic of Padé approximants to the exponential function

John Cullinan, Nick Scheel

The $(u, v)$ -Padé approximation to a function $f$ is the (unique, up to scaling) rational approximation $f (x) = P (x) / Q (x) + O (x^{u + v + 1})$ , where $P$ has degree $u$ and $Q$ has degre…

math.NT2020

On a probabilistic local-global principle for torsion on elliptic curves

John Cullinan, Meagan Kenney, John Voight

Let $m$ be a positive integer and let $E$ be an elliptic curve over $Q$ with the property that $m\mid#E(\mathbb{F}_p)$ for a density $1$ set of primes $p$ . Building upon w…

math.NT2019★ 1 cited

Divisibility of torsion subgroups of abelian surfaces over number fields

John Cullinan, Jeffrey Yelton

Let $A$ be a 2-dimensional abelian variety defined over a number field $K$ . Fix a prime number $ℓ$ and suppose $# A (F_{p}) \equiv 0 (mod ℓ^{2})$ for a set of primes $\m…