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The spectral decomposition of a product of automorphic forms


Author: C. J. Moreno
Journal: Proc. Amer. Math. Soc. 88 (1983), 399-403
MSC: Primary 10D40; Secondary 10D12
DOI: https://doi.org/10.1090/S0002-9939-1983-0699402-8
MathSciNet review: 699402
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Abstract: The spectral theory of Roelke and Selberg provides a decomposition of the space of square integrable automorphic forms for the group $ SL(2)$ in terms of eigenfunctions of the non-Euclidean Laplacian and of the Hecke operators. The main result of the paper uses the Roelke-Selberg theory to give an interpretation of the $ L$-functions of Rankin type as "multiplicity factors" in the decomposition of the product of a nonholomorphic Eisenstein series and a cusp form.


References [Enhancements On Off] (What's this?)

  • [1] Tomio Kubota, Elementary theory of Eisenstein series, Kodansha Ltd., Tokyo; Halsted Press [John Wiley & Sons], New York-London-Sydney, 1973. MR 0429749
  • [2] Carlos Julio Moreno, The Petersson inner product and the residue of an Euler product, Pacific J. Math. 78 (1978), no. 1, 149–155. MR 513290

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0699402-8
Article copyright: © Copyright 1983 American Mathematical Society