Jaclyn Lang

activity

20092026

most citedOn the image of the Galois representation associated to a non-CM Hida family

9 citations · 9 across the 9 of their papers we have counts for

collaborators

10 papers

math.NT2026

Counting level-raising congruences using modular representation theory

Jaclyn Lang, Robert Pollack, Preston Wake

We introduce a new method for studying mod- $ℓ$ congruences between eigenforms through the modular representation theory of $PGL_{2} (F_{p})$ . When $p\equiv \pm 1 \p…

math.NT2026

Modularity theorems for Eisenstein congruences in prime-power level

Jaclyn Lang, Katharina Müller, Bharathwaj Palvannan

Let $p, N \geq 5$ be primes such that $N \equiv 1 mod p$ . We prove modularity theorems at levels $N$ and $N^{2}$ , showing that suitable Eisenstein localizations of the weight- $2$ $…

math.NT2026

A new perspective on the rank of Mazur's Eisenstein Hecke algebra

Jaclyn Lang, Katharina Müller, Bharathwaj Palvannan

Let $N, p \geq 5$ be primes such that $N \equiv 1 mod p$ . We study the rank $r$ of the Hecke algebra that parametrizes modular forms of weight 2 and level $N$ that are Eisenstein…

math.NT2025

The Eisenstein ideal at prime-square level has constant rank

Jaclyn Lang, Preston Wake

Let $N$ and $p$ be prime numbers with $p \geq 5$ such that $p ∣∣ (N + 1)$ . In a previous paper, we showed that there is a cuspform $f$ of weight 2 and level $Γ_{0} (N^{2})$ whose $ℓ$ …

math.NT2021

A modular construction of unramified $p$ -extensions of $Q (N^{1/ p})$

Jaclyn Lang, Preston Wake

We show that for primes $N, p \geq 5$ with $N \equiv - 1 mod p$ , the class number of $Q (N^{1/ p})$ is divisible by $p$ . Our methods are via congruences between Eisenstein…

math.NT2019

Big images of two-dimensional pseudorepresentations

Andrea Conti, Jaclyn Lang, Anna Medvedovsky

Bellaïche has recently applied Pink-Lie theory to prove that, under mild conditions, the image of a continuous 2-dimensional pseudorepresentation $ρ$ of a profinite group on a loca…

math.NT2017

Chow motives associated to certain algebraic Hecke characters

Laure Flapan, Jaclyn Lang

Shimura and Taniyama proved that if $A$ is a potentially CM abelian variety over a number field $F$ with CM by a field $K$ linearly disjoint from F, then there is an algebraic Heck…

math.NT2016

Shadow lines in the arithmetic of elliptic curves

Jennifer S. Balakrishnan, Mirela Ciperiani, Jaclyn Lang +2

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a correspond…

math.NT2014★ 9 cited

On the image of the Galois representation associated to a non-CM Hida family

Jaclyn Lang

Fix a prime $p > 2$ . Let $ρ : Gal (Q / Q) \to GL_{2} (I)$ be the Galois representation coming from a non-CM irreducible component $\mat…

math.NT2009

Function Fields with Class Number Indivisible by a Prime $ℓ$

Michael Daub, Jaclyn Lang, Mona Merling +3

It is known that infinitely many number fields and function fields of any degree $m$ have class number divisible by a given integer $n$ . However, significantly less is known about…

Counting level-raising congruences using modular representation theory

Modularity theorems for Eisenstein congruences in prime-power level

A new perspective on the rank of Mazur's Eisenstein Hecke algebra

The Eisenstein ideal at prime-square level has constant rank

A modular construction of unramified p-extensions of Q(N1/p)

Big images of two-dimensional pseudorepresentations

Chow motives associated to certain algebraic Hecke characters

Shadow lines in the arithmetic of elliptic curves

On the image of the Galois representation associated to a non-CM Hida family

Function Fields with Class Number Indivisible by a Prime ℓ

A modular construction of unramified $p$ -extensions of $Q (N^{1/ p})$

Function Fields with Class Number Indivisible by a Prime $ℓ$