# On exceptional eigenvalues of the Laplacian for $\Gamma_0(N)$

@article{Li2006OnEE,
title={On exceptional eigenvalues of the Laplacian for \$\Gamma_0(N)\$},
author={X. Li},
journal={arXiv: Number Theory},
year={2006}
}
• X. Li
• Published 2006
• Mathematics
• arXiv: Number Theory
• An explicit Dirichlet series is obtained, which represents an analytic function of $s$ in the half-plane $\Re s>1/2$ except for having simple poles at points $s_j$ that correspond to exceptional eigenvalues $\lambda_j$ of the non-Euclidean Laplacian for Hecke congruence subgroups $\Gamma_0(N)$ by the relation $\lambda_j=s_j(1-s_j)$ for $j=1,2,..., S$. Coefficients of the Dirichlet series involve all class numbers $h_d$ of real quadratic number fields. But, only the terms with \$h_d\gg d^{1/2… CONTINUE READING

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His primary research interests include data mining, machine learning, bioinformatics, and music information retrieval. He is on the editorial board for
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Lectures on Number Theory
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