Trace formulae and applications to class numbers

Author:

Raulf Nicole

Abstract

AbstractIn this paper we compute the trace formula for Hecke operators acting on automorphic forms on the hyperbolic 3-space for the group PSL2($\mathcal{O}_K $) with $\mathcal{O}_K $ being the ring of integers of an imaginary quadratic number field K of class number H K > 1. Furthermore, as a corollary we obtain an asymptotic result for class numbers of binary quadratic forms.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference24 articles.

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2. Bauer-Price P., The Selberg Trace Formula for PSL(2, $\mathcal{O}_K $ ) for Imaginary Quadratic Number Fields K of Arbitrary Class Number, Bonner Math. Schriften, 221, Universität Bonn, 1991

3. Deitmar A., Hoffmann W., Asymptotics of class numbers, Invent. Math., 2005, 160(3), 647–675

4. Efrat I.Y., The Selberg Trace Formula for PSL2(ℝ)n, Mem. Amer. Math. Soc., 65(359), American Mathematical Society, Providence, 1987

5. Elstrodt J., Grunewald F., Mennicke J., Groups Acting on Hyperbolic Space, Springer Monogr. Math., Springer, Berlin, 1998

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