The Central value of the Rankin-Selberg L -Functions

Author： Li Xiaoqing  

Publisher： Springer Publishing Company

ISSN： 1016-443X

Source： Geometric & Functional Analysis GAFA, Vol.18, Iss.5, 2009-02, pp. : 1660-1695

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Abstract

Let f be a Maass form for SL $$(3, {mathbb{Z}})$$ which is fixed and u j be an orthonormal basis of even Maass forms for SL $$(2, {mathbb{Z}})$$ , we prove an asymptotic formula for the average of the product of the Rankin-Selberg L-function of f and u j and the L-function of u j at the central value 1/2. This implies simultaneous nonvanishing results of these L-functions at 1/2.

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