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Spectrum of the Laplace-Beltrami operator for certain congruence subgroups of the modular group


Authors: V. V. Golovchanskiĭ and M. N. Smotrov
Translated by: A. Plotkin
Original publication: Algebra i Analiz, tom 23 (2011), nomer 4.
Journal: St. Petersburg Math. J. 23 (2012), 659-664
MSC (2010): Primary 11F72
DOI: https://doi.org/10.1090/S1061-0022-2012-01212-4
Published electronically: April 13, 2012
MathSciNet review: 2893520
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that, up to multiplicity, the spectra of automorphic Laplacians coincide in the case of the pairs of congruence subgroups $ \{\Gamma _0(16N),\Gamma _0(8N)\}$ and $ \{\Gamma _0(64N), \Gamma _0(32N)\}$ of the modular group, where $ N$ is an odd integer. A formula is obtained for the dimension of the subspaces of automorphic forms for the subgroups $ \Gamma _0(16N)$ and $ \Gamma _0(64N)$.


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Additional Information

V. V. Golovchanskiĭ
Affiliation: Khabarovsk Department, Institute of Applied Mathematics, Dzerzhinskiĭ Street 54, Khabarovsk 680000, Russia
Email: gsm@iam.khv.ru

M. N. Smotrov
Affiliation: Khabarovsk Department, Institute of Applied Mathematics, Dzerzhinskiĭ Street 54, Khabarovsk 680000, Russia

DOI: https://doi.org/10.1090/S1061-0022-2012-01212-4
Keywords: Automorphic forms, Selberg’s zeta function, congruence subgroups, Laplace–Beltrami operator, Selberg trace formula
Received by editor(s): February 17, 2010
Published electronically: April 13, 2012
Article copyright: © Copyright 2012 American Mathematical Society

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