Xue Hui

activity

20242026

collaborators

5 papers

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…