The spectral decomposition of a product of automorphic forms
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- by C. J. Moreno PDF
- Proc. Amer. Math. Soc. 88 (1983), 399-403 Request permission
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
- Tomio Kubota, Elementary theory of Eisenstein series, Kodansha, Ltd., Tokyo; Halsted Press [John Wiley & Sons, Inc.], New York-London-Sydney, 1973. MR 0429749
- 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
Additional Information
- © Copyright 1983 American Mathematical Society
- 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