The central value of the Rankin-Selberg L-functions
نویسنده
چکیده
The values of L-functions at special points have been the subject of intensive studies. For example, a good positive lower bound for the central value of Hecke L-functions would rule out the existence of the Landau-Siegel zero, see the notable paper [IS]; the nonvanishing of certain Rankin-Selberg L-functions is a crucial ingredient in the current development of the generalized Ramanujan conjecture [LRS], etc. In this paper, we consider the simultaneous nonvanishing problem of products of Rankin-Selberg on GL(3) and GL(2) and Maass Lfunctions on GL(2) at the central point 1/2. Specifically, let uj(z) be an orthonormal basis of even Hecke-Maass forms for the modualr group SL(2,Z). For each uj(z), let aj(n) be its normalized Fourier coefficients (see the next section), we associate the L-function:
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