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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)

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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

Abstract:

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: holger.then@physik.uni-ulm.de
  • 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: https://doi.org/10.1090/S0025-5718-04-01658-8
  • MathSciNet review: 2085897