Erick Ross

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20242026

most citedAsymptotics and sign patterns of Hecke polynomial coefficients

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

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18 papers · 1 filter

math.NT2026

Unconditional Bounds for Two, Three and Four Consecutive Moderate Gaps between Zeros of the Riemann Zeta Function

César Angón, Erick Ross, Ze Sen Tang +1

We prove unconditional positive-proportion results for consecutive moderate gaps between zeros of the Riemann zeta function. More precisely, for every fixed $0<c\leq 1/4$, the lo…

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

Interlacing for zeros of the Serre derivative of Eisenstein series

Maggie Bohanek, Owen McGinty, Erick Ross +2

In 1970, Rankin and Swinnerton-Dyer showed that the non-elliptic zeros of Eisenstein series $E_{k}$ in the fundamental domain all lie on the lower arc $\{ e^{iθ}: \fracπ{2} < θ< \fra…

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.NT2026

Boundary CM points and class groups of small exponent

David Aiken, Erick Ross, Dmitriy Shvydkoy +1

Let $F$ denote the fundamental domain for $SL_{2} (Z)$ on the upper half plane $H$ . William Duke showed that as fundamental discriminants $D \to -\in…

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…

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…