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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the existence of Maass cusp forms on hyperbolic surfaces with cone points
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by Christopher M. Judge PDF
J. Amer. Math. Soc. 8 (1995), 715-759 Request permission

Abstract:

The perturbation theory of the Laplace spectrum of hyperbolic surfaces with conical singularities belonging to a fixed conformal class is developed. As an application, it is shown that the generic such surface with cusps has no Maass cusp forms (${L^2}$ eigenfunctions) under specific eigenvalue multiplicity assumptions. It is also shown that eigenvalues depend monotonically on the cone angles. From this, one obtains Neumann eigenvalue monotonicity for geodesic triangles in ${{\mathbf {H}}^2}$ and a lower bound of $\frac {1}{2}{\pi ^2}$ for the eigenvalues of ‘odd’ Maass cusp forms associated to Hecke triangle groups.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 8 (1995), 715-759
  • MSC: Primary 11F72; Secondary 58G25
  • DOI: https://doi.org/10.1090/S0894-0347-1995-1273415-6
  • MathSciNet review: 1273415