Erick Ross

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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.NT2025

Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus

Erick Ross

Fix a prime $p$ , and let $T_{p}^{new} (N, k, χ) := χ (p)^{- 1/2} p^{- (k - 1) /2} T_{p}^{new} (N, k, χ)$ denote the normalized $p$ 'th Hecke operator over the newspace wi…

math.NT2025

Dimension sequences of modular forms

Erick Ross

For $N \geq 1$ , let $S_{2}^{new} (N)$ denote the newspace of cuspidal modular forms of weight $2$ and level $N$ . In 2004, Greg Martin conjectured that as a sequence in $N$ , $…

math.NT2024

Non-repetition of second coefficients of Hecke polynomials

Archer Clayton, Helen Dai, Tianyu Ni +3

Let $T_{m} (N, 2 k)$ denote the $m$ -th Hecke operator on the space $S_{2 k} (Γ_{0} (N))$ of cuspidal modular forms of weight $2 k$ and level $N$ . In this paper, we study the non-repetition of…