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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0699402-8
PII: S 0002-9939(1983)0699402-8
Article copyright: © Copyright 1983 American Mathematical Society