John Cullinan

collaborators

3 papers

math.NT2024

On the discriminants of truncated logarithmic polynomials

John Cullinan, Rylan Gajek-Leonard

We provide evidence for a conjecture of Yamamura that the truncated logarithmic polynomials \[ F_n(x) = 1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n} \] have Galois group $S_{n}$ fo…

math.NT2024

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

John Cullinan, Shanna Dobson, Linda Frey +5

Let $E$ and $E^{'}$ be 2-isogenous elliptic curves over $\Q$. Following \cite{ck}, we call a good prime $p$ \emph{anomalous} if $E(\F_p) \simeq E'(\F_p)$ but $E(\F_{p^2}) \not \simeq…

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…