Author

Erick Ross

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Preprint Sep 2026

Only finitely many modular Jacobians are supersingular modulo a given prime

In this paper, we study supersingularity of modular Jacobians $J_0(N)$ and abelian varieties $A_f$ of $\mathrm{GL}_{2}$-type from both the vertical perspective (where the prime $p$ is fixed, and the level $N$ varies) and the horizontal perspective (where the newform $f$ is fixed, and the prime $p$ varies). Vertically,...

Aarya J. Kumar, Sargam Mondal, Erick Ross et al. · 0 citations

Preprint Sep 2026

Effective Hecke eigenvalue equidistribution over the Atkin--Lehner subspaces

For a fixed prime $p$, let $\mu_p$ denote the $p$-adic Plancherel measure. Then the first main goal of this paper is to prove effective (and moreover explicit) $\mu_p$-equidistribution of the $p$-th Hecke eigenvalues over the Atkin--Lehner subspaces $S_k^\sigma(N) \subseteq S_k(N)$ and $S_k^{\operatorname{new}, \sigma}...

Aarya J. Kumar, Sargam Mondal, Erick Ross et al. · 2 citations

Preprint Aug 2026

Asymptotics of Hecke polynomial coefficients on the Atkin-Lehner eigenspaces

Let $S_k^\sigma(N)$ denote the space of cusp forms of level $N$, weight $k$, and Atkin-Lehner sign pattern $\sigma$, and $S_k^{\mathrm{new},\sigma}$ denote its new subspace. In this paper, we study the asymptotic behavior of the coefficients of the $m$-th Hecke polynomial over $S_k^\sigma(N)$ and $S_k^{\mathrm{new},\si...

Timothy Nelson, Erick Ross, Maya Wassercug et al. · 0 citations