Author:
Lau Yuk-Kam,Ng Ming Ho,Wang Yingnan
Abstract
Abstract
A two-dimensional central limit theorem for the eigenvalues of
{\mathrm{GL}(n)}
Hecke–Maass cusp forms is newly derived. The covariance matrix is diagonal and hence verifies the statistical independence between the real and imaginary parts of the eigenvalues. We also prove a central limit theorem for the number of weighted eigenvalues in a compact region of the complex plane, and evaluate some moments of eigenvalues for the Hecke operator
{T_{p}}
which reveal interesting interferences.
Funder
Research Grants Council, University Grants Committee
National Natural Science Foundation of China
Natural Science Foundation of Guangdong Province
Subject
Applied Mathematics,General Mathematics
Cited by
3 articles.
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