42
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Numerical Computations of Green's Function and Its Fourier Coefficients on PSL(2, ℤ)

Pages 335-343 | Received 27 Sep 2007, Accepted 25 Aug 2009, Published online: 11 Feb 2011

REFERENCES

  • Avelin , H. 2007 . “Computations of the Green's Function and Its Fourier Coefficients on PSL(2, Z).” Available online http://www.math.uu.se/research/pub/Avelin5.pdf[Avelin 07a]
  • Avelin , H. 2007 . “Topography of the Green's Function and Its Fourier Coefficients on PSL(2, Z).” Available online http://www.math.uu.se/research/archive/avelin/greendata/Topography_Green.pdf, [Avelin 07b]
  • Avelin , H. 2008 . “Computations of Eisenstein Series on Fuchsian Groups.” . Math. Comp. , 77 : 1779 – 1800 . [Avelin 08]
  • Avelin , H. 2010 . “Computations of Green's Function and Its Fourier Coefficients on Fuchsian Groups.” . Exp. Math. , 19 ( 3 ) : 317 – 334 . [Avelin 10]
  • Booker , A. , Strömbergsson , A. and Venkatesh , A. 2006 . “Effective Computations of Maass Cusp Forms.” . Int. Math. Res. Not. , : 34pp. Art. ID 71281. [Booker et al. 06]
  • Vries , P. , van de Coevorden , D. V. and Lagendijk , A. 1998 . “Point Scatterers for Classical Waves.” . Reviews of Modern Physics , 70 ( 2 ) : 447 – 466 . [de Vries et al. 98]
  • Hejhal , D. A. 1981 . “Some Observations Concerning Eigenvalues of the Laplacian and Dirichlet L-Series.” . In Recent Progress in Analytic Number Theory vol. 2 , 95 – 110 . New York : Academic Press. . [Hejhal 81]
  • Hejhal , D. A. 1983 . The Selberg Trace Formula for PSL(2, R), vol. 2, Lecture Notes in Math. 1001 Berlin : Springer. . [Hejhal 83]
  • Hejhal , D. A. 1992 . Eigenvalues of the Laplacian for Hecke Triangle Groups Providence : AMS. . Mem. Amer. Math. Soc. 469, [Hejhal 92]
  • Hejhal , D. A. 1999 . “On Eigenfunctions of the Laplacian for Hecke Triangle Groups.” . In Emerging Applications of Number Theory Edited by: Hejhal , D. , Friedman , J. , Gutzwiller , M. and Odlyzko , A. 291 – 315 . New York : Springer. . [Hejhal 99]
  • Hejhal , D. A. and Rackner , B. N. 1992 . “On the Topography of Maass Waveforms for PSL(2, Z).” . Exp. Math. , 1 ( 4 ) : 275 – 305 . [Hejhal and Rackner 92]
  • Hejhal , D. A. and Strömbergsson , A. 2001 . “On Quantum Chaos and Maass Waveforms of CM-Type.” . Found. Phys. , 31 ( 3 ) : 519 – 533 . [Hejhal and Strömbergsson 01]
  • Šeba , P. 1990 . “Wave Chaos in Singular Quantum Billiard.” . Physical Review Letters , 64 ( 16 ) : 1855 – 1858 . [Šeba 90]
  • Shigehara , T. 1994 . “Conditions for the Appearance of Wave Chaos in Quantum Singular Systems with a Pointlike Scatterer.” . Phys. Rev. E , 50 : 4357 – 4370 . [Shigehara 94]
  • Shigehara , T. and Cheon , T. 1997 . “Spectral Properties of Three-Dimensional Quantum Billiards with a Pointlike Scatterer.” . Phys. Rev. E , 55 : 6832 – 6844 . [Shigehara and Cheon 97]

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.