Hui Xue

collaborators

11 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

Explicit generators of the space of modular forms

Tianyu Ni, Ashley Song, Yanhui Su +2

Let $S_{I^} º$ be the space of cusp forms of weight $I^º$ and level one, and let $S_{I^} º^{*}$ denote its dual space. In this paper, we find explicit spanning subsets of $S_{I^} º$ consisti…

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.NT2026

Twisted periods of modular forms

Tianyu Ni, Hui Xue

Let $S_{k}$ denote the space of cusp forms of weight $k$ and level one. For $0 \leq t \leq k - 2$ and primitive Dirichlet character $I ¨ $ mod $D$ , we introduce twisted periods $r_{t, I ¨ }$ …