## On a relation between $\widetilde {\mathrm {SL}}_{2}$ cusp forms and cusp forms on tube domains associated to orthogonal groups

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- by S. Rallis and G. Schiffmann
- Trans. Amer. Math. Soc.
**263**(1981), 1-58 - DOI: https://doi.org/10.1090/S0002-9947-1981-0590410-7
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## Abstract:

We use the decomposition of the discrete spectrum of the Weil representation of the dual reductive pair $({\tilde {SL}_2},\;O(Q))$ to construct a generalized Shimura correspondence between automorphic forms on $O(Q)$ and $\widetilde {S{L_2}}$. We prove a generalized Zagier identity which gives the relation between Fourier coefficients of modular forms on $\widetilde {S{L_2}}$ and $O(Q)$. We give an explicit form of the lifting between $\widetilde {S{L_2}}$ and $O(n,2)$ in terms of Dirichlet series associated to modular forms. For the special case $n = 3$, we construct certain Euler products associated to the lifting between $S{L_2}$ and ${\text {S}}{{\text {p}}_2} \cong O(3,2)$ (locally).## References

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## Bibliographic Information

- © Copyright 1981 American Mathematical Society
- 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