Xue Hui

activity

20112026

most citedProducts of Nearly Holomorphic Eigenforms

11 citations · 11 across the 6 of their papers we have counts for

collaborators

9 papers

math.NT2026

Only finitely many modular Jacobians are supersingular modulo a given prime

Aarya J. Kumar, Sargam Mondal, Erick Ross +1

In this paper, we study supersingularity of modular Jacobians $J_{0} (N)$ and abelian varieties $A_{f}$ of $GL_{2}$ -type from both the vertical perspective (where the prime $p$ …

math.NT2026

Effective Hecke eigenvalue equidistribution over the Atkin--Lehner subspaces

Aarya J. Kumar, Sargam Mondal, Erick Ross +1

For a fixed prime $p$ , let $μ_{p}$ denote the $p$ -adic Plancherel measure. Then the first main goal of this paper is to prove effective (and moreover explicit) $μ_{p}$ -equidistribution…

math.NT2026

On murmurations

Timothy Nelson, Erick Ross, Maya Wassercug +1

In the recent paper ``Murmurations", Zubrilina showed that the Fourier coefficients of modular forms follow a certain murmuration pattern. The proof given in ``Murmurations" procee…

math.NT2026

Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces

Timothy Nelson, Erick Ross, Maya Wassercug +1

Let $S_{k}^{σ} (N)$ denote the space of cusp forms of level $N$ , weight $k$ , and Atkin-Lehner sign pattern $σ$ , and $S_{k}^{new, σ}$ denote its new subspace. In this paper, we stu…

math.NT2026

Equidistribution of CM points and RM curves

Erick Ross, Hui Xue

In 1988, William Duke showed that CM points of fundamental discriminant $D$ are equidistributed in the complex upper half-plane $H$ as $D \to - \infty$ . He also showed a si…

math.NT2025

Proportion of Atkin-Lehner sign patterns and Hecke Eigenvalue Equidistribution

Erick Ross, Alexandre van Lidth, Martha Rose Wolf +1

Let $N \geq 1$ , $k \geq 2$ even, and $σ$ denote a sign pattern for $N$ . In this paper, we first determine the exact proportion of forms in $S_{k} (N)$ and $S_{k}^{new} (N)$ with a g…

math.NT2024

Signs of the Second Coefficients of Hecke Polynomials

Erick Ross, Hui Xue

Let $T_{m} (N, k, χ)$ be the $m$ -th Hecke operator of level $N$ , weight $k \geq 2$ , and nebentypus $χ$ , where $N$ is coprime to $m$ . We first show that for any given $m \geq 1$ , the sec…

math.NT2024

Nonvanishing of Second Coefficients of Hecke Polynomials on the Newspace

William Cason, Akash Jim, Charlie Medlock +3

For $m \geq 1$ , let $N \geq 1$ be coprime to $m$ , $k \geq 2$ , and $χ$ be a Dirichlet character modulo $N$ with $χ (- 1) = (- 1)^{k}$ . Then let $T_{m}^{new} (N, k, χ)$ denote the restric…

math.NT2011★ 11 cited

Products of Nearly Holomorphic Eigenforms

Jeffrey Beyerl, Kevin James, Catherine Trentacoste +1

We prove that the product of two nearly holomorphic Hecke eigenforms is again a Hecke eigenform for only finitely many choices of factors.