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

Ginzburg, David; Jiang, Dihua; Rallis, Stephen

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

On the nonvanishing of the central value of the Rankin-Selberg $L$-functions
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by David Ginzburg, Dihua Jiang and Stephen Rallis

J. Amer. Math. Soc. 17 (2004), 679-722

DOI: https://doi.org/10.1090/S0894-0347-04-00455-2

Published electronically: April 1, 2004

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Abstract:

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.

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