Rylan Gajek-Leonard

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20232026

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math.NT2024

A bound on the $μ$ -invariants of supersingular elliptic curves

Rylan Gajek-Leonard

Let $E / Q$ be an elliptic curve and let $p$ be a prime of good supersingular reduction. Attached to $E$ are pairs of Iwasawa invariants $μ_{p}^{\pm}$ and $λ_{p}^{\pm}$ which encode…

math.NT2024

Stretching Newton polygons using pure polynomials

Rylan Gajek-Leonard, Uri Tomer

The $p$ -adic Newton polygon is a visual tool that encodes information about the roots and factorization of a polynomial relative to a prime $p$ . In this article, we investigate how…

math.NT2024

Entanglement of elliptic curves upon base extension

Tori Day, Rylan Gajek-Leonard

Fix distinct primes $p$ and $q$ and let $E$ be an elliptic curve defined over a number field $K$ . The $(p, q)$ -entanglement type of $E$ over $K$ is the isomorphism class of the grou…

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

On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in $Z_{p}$ -extensions

Rylan Gajek-Leonard, Jeffrey Hatley, Debanjana Kundu +1

Let $p$ be an odd prime. We study Mazur's conjecture on the growth of the Mordell--Weil ranks of an elliptic curve $E / Q$ over $Z_{p}$ -extensions of an imaginary qua…

A bound on the μ-invariants of supersingular elliptic curves

Stretching Newton polygons using pure polynomials

Entanglement of elliptic curves upon base extension

On the discriminants of truncated logarithmic polynomials

On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in Zp​-extensions

A bound on the $μ$ -invariants of supersingular elliptic curves

On a conjecture of Mazur predicting the growth of Mordell--Weil ranks in $Z_{p}$ -extensions