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

Author:

Ginzburg David,Jiang Dihua,Rallis Stephen

Abstract

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

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference53 articles.

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3. [BFSP04]BFSP04 Boecherer, S.; Furusawa, M.; Schulze-Pillot, R. On the global Gross-Prasad conjecture for Yoshida liftings. Contributions to Automorphic Forms, Geometry, and Number Theory. The Johns Hopkins University Press, 2004.

4. On lifting from classical groups to 𝐺𝐿_{𝑁};Cogdell, J. W.;Publ. Math. Inst. Hautes \'{E}tudes Sci.,2001

5. [CKPSS]CKPSS Cogdell, J.; Kim, H.; Piatetski-Shapiro, I.; Shahidi, F. Functoriality for the classical groups. To appear in Inst. Hautes Études Sci. Publ. Math.

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