Erick Ross

activity

20242026

most citedAsymptotics and sign patterns of Hecke polynomial coefficients

3 citations · 3 across the 14 of their papers we have counts for

collaborators

Showing 2024Show all

7 papers · 1 filter

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…

math.NT2024★ 3 cited

Asymptotics and sign patterns of Hecke polynomial coefficients

Erick Ross, Hui Xue

We determine the asymptotic behavior of the coefficients of Hecke polynomials. In particular, this allows us to determine signs of these coefficients when the level or the weight i…

math.NT2024

Zeros of even and odd period polynomials

Grace Ko, Jennifer Mackenzie, Erick Ross +1

Let $f \in S_{k} (Γ_{0} (N))$ be a newform, and let $r_{f}^{\pm} (X)$ denote its corresponding even and odd period polynomials. For sufficiently large level and weight, we show that the zer…

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

On the average size of the eigenvalues of the Hecke operators

William Cason, Akash Jim, Charlie Medlock +2

We determine the average size of the eigenvalues of the Hecke operators acting on the cuspidal modular forms space $S_{k} (Γ_{0} (N))$ in both the vertical and the horizontal perspective…

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.NT2024

Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces

Erick Ross

Consider $N \geq 1$ , $k \geq 2$ , and $χ$ a Dirichlet character modulo $N$ such that $χ (- 1) = (- 1)^{k}$ . For any bound $B$ , one can show that $dim S_{k} (Γ_{0} (N), χ) \leq B$ for only finit…