The second moment of GL3×GL2L-functions at special points - Qi, Zhi (Mathematische annalen, 2025)
Let ϕ be a fixed Hecke–Maass form for SL3(Z) and uj traverse an orthonormal basis of Hecke–Maass forms for SL2(Z). Let 1/4+tj2 be the Laplace eigenvalue of uj. In this paper, we prove the mean Lindelöf hypothesis for the second moment of L(1/2+itj,ϕ×uj) on T<tj⩽T+T. Previously, this was proven by Young on tj⩽T. Our approach is more direct as we do not apply the Poisson summation formula to detect the ‘Eisenstein–Kloosterman’ cancellation.