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Traces of Hecke operators acting on three-dimensional hyperbolic space
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Nicole Raulf
Published/Copyright:
May 8, 2006
Abstract
The goal of this paper is to derive a number theoretic expression for the trace trλTv of the Hecke operator Tv acting on the eigenspace ℰλ for the eigenvalue λ = 1 + κ2 > 0 of −Δ. We obtain that the trace can be expressed as the residue of a certain linear combination of L-series. Furthermore, the analytic behaviour of this combination gives information on the asymptotic behaviour of the class number.
Received: 2005-01-06
Published Online: 2006-05-08
Published in Print: 2006-02-24
© Walter de Gruyter
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Articles in the same Issue
- Three-dimensional exponential sums with monomials
- A Fourier transformation for Higgs bundles
- Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane
- Kähler quantization and reduction
- Traces of Hecke operators acting on three-dimensional hyperbolic space
- Teitelbaum's exceptional zero conjecture in the function field case
- Symmetries, quotients and Kähler-Einstein metrics
- Smoothing of ribbons over curves
Articles in the same Issue
- Three-dimensional exponential sums with monomials
- A Fourier transformation for Higgs bundles
- Pucci's conjecture and the Alexandrov inequality for elliptic PDEs in the plane
- Kähler quantization and reduction
- Traces of Hecke operators acting on three-dimensional hyperbolic space
- Teitelbaum's exceptional zero conjecture in the function field case
- Symmetries, quotients and Kähler-Einstein metrics
- Smoothing of ribbons over curves
