Journal of Soviet Mathematics

, Volume 52, Issue 3, pp 3022–3025 | Cite as

Poincaré series in SL(3, R)

  • A. I. Vinogradov


It is shown that in the spectral decomposition of the one-parameter Poincaré series from SL(3, R) involves only the discrete spectrum, induced from SL2 and not the discrete spectrum of SL3 itself.


Discrete Spectrum Spectral Decomposition 
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Literature cited

  1. 1.
    A. I. Vinogradov and L. A. Takhtadzhyan, “The theory of the Eisenstein series for the group SL(3, R) and its application to a binary problem. I. Fourier expansion of the highest Eisenstein series”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,76, 5–52 (1978).MathSciNetGoogle Scholar
  2. 2.
    N. V. Proskurin, “On automorphic functions on SL(m, R)”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,129, 164–176 (1983).MATHMathSciNetGoogle Scholar
  3. 3.
    D. Goldfeld, “Poincaré series for SL(3, ℤ)”, Séminaire Théorie Nombres de Bordeaux, 1983–1984, pp. 17.01–17.06.Google Scholar

Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • A. I. Vinogradov

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