Rylan Gajek-Leonard

activity

20232026

collaborators

8 papers

math.NT2026

A canonical construction of signed $p$ -adic $L$ -functions for non-ordinary modular forms of weight $\leq p + 1$

Rylan Gajek-Leonard, Antonio Lei

Fix an odd prime $p$ and let $f$ be a $p$ -non-ordinary cuspidal eigen-newform of weight $2 \leq k \leq p + 1$ . We construct a pair of bounded $p$ -adic $L$ -functions associated to $f$ b…

math.NT2025

Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two

Rylan Gajek-Leonard, Antonio Lei

Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$ . Assuming $p > k - 1$ , we compute asymptotic formulas for the Iwasawa invariant…

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…

math.NT2023

Iwasawa invariants of modular forms with $a_{p} = 0$

Rylan Gajek-Leonard

Fix a prime $p$ and a cuspidal newform $f$ of level coprime to $p$ with $a_{p} = 0$ . Attached to $f$ are signed $p$ -adic $L$ -functions $L_{p}^{\pm} (f)$ and Mazur-Tate elements $θ_{n} (f)$ , bo…

A canonical construction of signed p-adic L-functions for non-ordinary modular forms of weight ≤p+1

Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two

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

Iwasawa invariants of modular forms with ap​=0

A canonical construction of signed $p$ -adic $L$ -functions for non-ordinary modular forms of weight $\leq p + 1$

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

Iwasawa invariants of modular forms with $a_{p} = 0$