On the nonnegativity of Rankin-Selberg L-functions at the center of symmetry

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Automorphic period and the central value of Rankin--Selberg L-function (2012, methodology): “Lapid has obtained a more general result for Rankin-Selberg central L-values by a different method ([32]; cf.”
Transfer of Siegel Cusp Forms of Degree 2 (2011, result): “By combining our lifting results with the results of [37], we prove non-negativity at s = 1/2 for the spin and the “spin× standard” L-function as well as for suitable L-functions on GSp4 × GL2 and GSp4 ×GL3; see Theorem 5.”
A conjecture on Whittaker-Fourier coefficients of cusp forms (2013, unknown): “re X′(π) is the group of Hecke characters ωsuch that π⊗ω= π. Let us see that S (π1,π2) = |X((π 1,π2))|. The transfer π1 ⊠π2 is cuspidal unless one of the following conditions holds ([Ram00], cf. also [Lap03] and [Kri12, Appendix]): (1) π1 is not dihedral (i.e., X′(π1) = 1) and π2 = π1 ⊗χfor some Hec”