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On the nonvanishing of the central value of the Rankin-Selberg  -functions |
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| Authors: | David Ginzburg Dihua Jiang Stephen Rallis |
| Affiliation: | School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, 69978 Israel ; School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455 ; Department of Mathematics, The Ohio State University, Columbus, Ohio 43210 |
| Abstract: | We characterize the nonvanishing of the central value of the Rankin-Selberg  -functions in terms of periods of Fourier-Jacobi type. This characterization is based on the Langlands philosophy on functoriality and on applications of invariant theory to automorphic representations. The result is the symplectic analog of the Gross-Prasad conjecture. |
| Keywords: | Special value $L$-function period automorphic form |
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