Xue Hui

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20242026

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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…