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Poincaré series in SL(3, R)

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Abstract

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.

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Literature cited

  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).

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  2. N. V. Proskurin, “On automorphic functions on SL(m, R)”, Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,129, 164–176 (1983).

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  3. D. Goldfeld, “Poincaré series for SL(3, ℤ)”, Séminaire Théorie Nombres de Bordeaux, 1983–1984, pp. 17.01–17.06.

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Authors
  1. A. I. Vinogradov
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 160, pp. 37–40, 1987.

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Vinogradov, A.I. Poincaré series in SL(3, R). J Math Sci 52, 3022–3025 (1990). https://doi.org/10.1007/BF02342919

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  • DOI: https://doi.org/10.1007/BF02342919

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