Skip to Main Content

Mathematics of Computation

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

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Deformations of Maass forms
HTML articles powered by AMS MathViewer

by D. W. Farmer and S. Lemurell PDF
Math. Comp. 74 (2005), 1967-1982 Request permission


We describe numerical calculations which examine the Phillips-Sarnak conjecture concerning the disappearance of cusp forms on a noncompact finite volume Riemann surface $S$ under deformation of the surface. Our calculations indicate that if the Teichmüller space of $S$ is not trivial, then each cusp form has a set of deformations under which either the cusp form remains a cusp form or else it dissolves into a resonance whose constant term is uniformly a factor of $10^{8}$ smaller than a typical Fourier coefficient of the form. We give explicit examples of those deformations in several cases.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2000): 11F03, 11F30
  • Retrieve articles in all journals with MSC (2000): 11F03, 11F30
Additional Information
  • D. W. Farmer
  • Affiliation: American Institute of Mathematics, 360 Portage Avenue, Palo Alto, California 94307
  • MR Author ID: 341467
  • Email:
  • S. Lemurell
  • Affiliation: Chalmers University of Technology, SE-412 96 Göteborg, Sweden
  • Email:
  • Received by editor(s): February 19, 2003
  • Received by editor(s) in revised form: April 30, 2004
  • Published electronically: April 15, 2005
  • Additional Notes: Research of the first author was supported in part by the National Science Foundation and the American Institute of Mathematics.
    Research of the second author was supported in part by “Stiftelsen för internationalisering av högre utbildning och forskning” (STINT)
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 74 (2005), 1967-1982
  • MSC (2000): Primary 11F03; Secondary 11F30
  • DOI:
  • MathSciNet review: 2164106