Work

Proportion of Atkin–Lehner sign patterns and Hecke eigenvalue equidistribution

Year: 2026

Type: article

Abstract: Let upper N greater than or equals 1 N ≥ 1 $N \ge 1$ , k greater than or equals 2 k ≥ 2 $k \ge 2$ even, and sigma σ $\sigma$ denote a sign pattern for N . In this paper, we first determine the exact proportion of forms in upper S Subscript k Baseline left parenthesis upper N right parenthesis S k ( N ) $S_k(N)$ and upper S Subscript k Superscript normal n normal e normal w Baseline left parenthesis upper N right parenthesis S k n e w ( N ) $S_k^{\mathrm{new}}(N)$ with a given Atkin–Lehner sign pattern sigma σ $\sigma$ . Then we study the asymptotic behaviour of the Hecke operators upper T Subscript p T p $T_p$ over the subspaces of upper S Subscript k Baseline left parenthesis upper N right parenthesis S k ( N

Source: Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/s0305004126101972

Authors: ERICK ROSS, ALEXANDRE VAN LIDTH, MARTHA ROSE WOLF, HUI XUE

Institutions: Clemson University, Amherst College, University of Michigan

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: National Science Foundation