On a relation between cusp forms and cusp forms on tube domains associated to orthogonal groups

Authors:
S. Rallis and G. Schiffmann

Journal:
Trans. Amer. Math. Soc. **263** (1981), 1-58

MSC:
Primary 10D40; Secondary 22E50, 32N10

DOI:
https://doi.org/10.1090/S0002-9947-1981-0590410-7

MathSciNet review:
590410

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Abstract | References | Similar Articles | Additional Information

Abstract: We use the decomposition of the discrete spectrum of the Weil representation of the dual reductive pair to construct a generalized Shimura correspondence between automorphic forms on and . We prove a generalized Zagier identity which gives the relation between Fourier coefficients of modular forms on and . We give an explicit form of the lifting between and in terms of Dirichlet series associated to modular forms. For the special case , we construct certain Euler products associated to the lifting between and (locally).

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DOI:
https://doi.org/10.1090/S0002-9947-1981-0590410-7

Article copyright:
© Copyright 1981
American Mathematical Society