On the nonvanishing of the central value of the Rankin-Selberg 𝐿-functions

Ginzburg, David¹ ; Jiang, Dihua² ; Rallis, Stephen³

¹School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, 69978 Israel
²School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
³Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Journal of the American Mathematical Society, Tome 17 (2004) no. 3, pp. 679-722

Résumé

We characterize the nonvanishing of the central value of the Rankin-Selberg $L$-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.

Détail

DOI : 10.1090/S0894-0347-04-00455-2

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