Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus

2025/11/17 by Ross, Erick
Mathematics · #11F72 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Primary: 11F11 #Random Matrices and Applications #Secondary: 11F25

paper · doi:10.48550/arxiv.2511.13966

openalex publication_date 2025/11/17 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

Fix a prime p, and let \widehat 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 with nenbentypus S_k^new(N,χ). In this paper, we determine the distribution of the eigenvalues of \widehat T_p^new(N,k,χ) as N+k → ∞.

Citations

• Nonvanishing of Second Coefficients of Hecke Polynomials on the Newspace
• Newspaces with Nebentypus: An Explicit Dimension Formula and Classification of Trivial Newspaces

Related

• The distribution of the eigenvalues of Hecke operators
• Effective joint distribution of eigenvalues of Hecke operators
• Bounds on the multiplicity of the Hecke eigenvalues
• On the average size of the eigenvalues of the Hecke operators
• Distribution of gaps between eigenangles of Hecke operators