Effective joint distribution of eigenvalues of Hecke operators

2017/03/23 by Sudhir Pujahari, Pujahari, Sudhir
Mathematics · #11R42 #11S40 #34L20 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1703.07944

openalex publication_date 2017/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In 1997, Serre proved that the eigenvalues of normalised p-th Hecke operator T^'_p acting on the space of cusp forms of weight k and level N are equidistributed in [-2,2] with respect to a measure that converge to the Sato-Tate measure, whenever N+k → ∞. In 2009, Murty and Sinha proved the effective version of Serre's theorem. In 2011, using Kuznetsov trace formula, Lau and Wang derived the effective joint distribution of eigenvalues of normalized Hecke operators acting on the space of primitive cusp forms of weight k and level 1. In this paper, we extend the result of Lau and Wang to space of cusp forms of higher level. Here we use Eichler-Selberg trace formula instead of Kuznetsov trace formula to deduce our result.

Related

• The distribution of the eigenvalues of Hecke operators
• Fluctuations in the distribution of Hecke eigenvalues about the\n Sato-Tate measure
• Eigenvalues of Hecke operators on Hilbert modular groups
• Hecke Eigenvalue Equidistribution over the Newspaces with Nebentypus
• On the average size of the eigenvalues of the Hecke operators