Spectrum of the Laplace–Beltrami operator for certain congruence subgroups of the modular group
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V. V. Golovchanskiĭ and M. N. Smotrov
Translated by: A. Plotkin - St. Petersburg Math. J. 23 (2012), 659-664
- DOI: https://doi.org/10.1090/S1061-0022-2012-01212-4
- Published electronically: April 13, 2012
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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 $\Gamma _0(64N)$.References
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Bibliographic 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
- Received by editor(s): February 17, 2010
- Published electronically: April 13, 2012
- © Copyright 2012 American Mathematical Society
- Journal: St. Petersburg Math. J. 23 (2012), 659-664
- MSC (2010): Primary 11F72
- DOI: https://doi.org/10.1090/S1061-0022-2012-01212-4
- MathSciNet review: 2893520