Rylan Gajek-Leonard

activity

20242026

collaborators

7 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.NT2026

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.NT2025

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 $I^¸_{n} (f)$ , b…

math.NT2025

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.NT2025

A bound on the $I^¼$ -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 $I^¼_{p}^{\pm}$ and $I^»_{p}^{\pm}$ which enco…

math.NT2025

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…

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

Iwasawa invariants of modular forms with ap​=0

Stretching Newton polygons using pure polynomials

A bound on the I^¼-invariants of supersingular elliptic curves

Entanglement of elliptic curves upon base extension

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

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

A bound on the $I^¼$ -invariants of supersingular elliptic curves