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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, The Artin-Takagi formula for Selberg zeta-functions and Roelcke's hypothesis, Dokl. Akad. Nauk SSSR 247 (1979), 540-543. (Russian) MR 545686 (84b:10042)

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

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