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Proceedings of the American Mathematical Society

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A remark on the multiplicity of the discrete spectrum of congruence groups


Author: Burton Randol
Journal: Proc. Amer. Math. Soc. 81 (1981), 339-340
MSC: Primary 58G25; Secondary 10D35
DOI: https://doi.org/10.1090/S0002-9939-1981-0593486-1
MathSciNet review: 593486
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Abstract: It is shown that the discrete spectrum of principal congruence groups of high level can contain eigenvalues of large multiplicity.


References [Enhancements On Off] (What's this?)

  • [1] E. Hecke, Uber ein fundamentalproblem aus der Theorie der elliptischen Modulfunktionen, Abh. Math. Sem. Univ. Hamburg 6 (1928), 235-257.
  • [2] H. W. Praetorius, Die Charaktere der Modulargruppen der Stufe $ {q^2}$, Abh. Math. Sem. Univ. Hamburg 9 (1933), 365-394.
  • [3] A. B. Venkov, Artin-Takagi formula for the Selberg zeta function and the Roelcke hypothesis, Dokl. Akad. Nauk SSSR 247 (1979), no. 3, 540–543 (Russian). MR 545686

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0593486-1
Article copyright: © Copyright 1981 American Mathematical Society