1 citations · 2 across the 10 of their papers we have counts for
11 papers
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 and occur as Galois groups over $\Q$. Hajir, i…
Kodaira-Neron statistics for rational elliptic curves with -invariant 0 and 1728
John Cullinan, Sebastian Sargenti
Elliptic curves over $\Q$ with -invariant 0 or 1728 have additive reduction at all primes of bad reduction. In addition, all elliptic curves with -invariant 0 have bad reduct…
The Gibbs phenomenon for the Krawtchouk polynomials
John Cullinan, Elisabeth Young
We study the Fourier approximation of the sign function by the Krawtchouk polynomials. We give numerical evidence that the Gibbs phenomenon of the approximation dif…
The probability of non-isomorphic group structures of isogenous elliptic curves in finite field extensions, I
John Cullinan, Nathan Kaplan
Let be a prime number and let and be -isogenous elliptic curves defined over a finite field of characteristic . Suppose the groups and…
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…
Towards a Universal Gibbs Constant
John Cullinan, Santanu Antu
In this paper we build on the work of \cite{kaber} where it was shown that the one-parameter family of Gegenbauer Polynomials (GP) exhibit a Gibbs Phenomenon at a jump discontinuit…
Realizations of Unisingular Representations by Hyperelliptic Jacobians
John Cullinan
A representation of a finite group on a finite dimensional vector space is called \textbf{unisingular} if every has 1 as an eigenvalue in its action on . In thi…
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…
On the arithmetic of Padé approximants to the exponential function
John Cullinan, Nick Scheel
The -Padé approximation to a function is the (unique, up to scaling) rational approximation , where has degree and has degre…
On a probabilistic local-global principle for torsion on elliptic curves
John Cullinan, Meagan Kenney, John Voight
Let be a positive integer and let be an elliptic curve over with the property that $m\mid#E(\mathbb{F}_p)$ for a density set of primes . Building upon w…
Divisibility of torsion subgroups of abelian surfaces over number fields
John Cullinan, Jeffrey Yelton
Let be a 2-dimensional abelian variety defined over a number field . Fix a prime number and suppose for a set of primes $\m…