Erick Ross

collaborators

13 papers

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 $I ¨ $ 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…

math.NT2025

Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus

Erick Ross

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