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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Maaß cusp forms for large eigenvalues
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by Holger Then PDF
Math. Comp. 74 (2005), 363-381 Request permission


We investigate the numerical computation of Maaß cusp forms for the modular group corresponding to large eigenvalues. We present Fourier coefficients of two cusp forms whose eigenvalues exceed $r=40000$. These eigenvalues are the largest that have so far been found in the case of the modular group. They are larger than the $130$millionth eigenvalue.
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Additional Information
  • Holger Then
  • Affiliation: Abteilung Theoretische Physik, Universität Ulm, 89069 Ulm, Germany
  • MR Author ID: 742378
  • ORCID: 0000-0002-0368-639X
  • Email:
  • Received by editor(s): November 26, 2002
  • Received by editor(s) in revised form: July 4, 2003
  • Published electronically: March 23, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 363-381
  • MSC (2000): Primary 11F72, 11F30; Secondary 11F12, 11Yxx, 11-4, 81Q50
  • DOI:
  • MathSciNet review: 2085897