Averages of shifted convolution sums for GL(3) x GL(2)

Let A(f) (1, n) be the normalized Fourier coefficients of a GL(3) Hecke Maass cusp forth f and let a(g)(n) be the normalized Fourier coefficients of a GL(2) cusp form g. Let lambda(n) be either Af (1, n) or the triple divisor function d(3)(n). It is proved that for any epsilon > 0, any integer r >= 1 and r(5/2)X(1/4+7 delta/2) <= H <= X with delta > 0, 1/H Sigma W-h >= 1 (h/H) Sigma(n >= 1) lambda(n)a(g) (rn + h)V (n/X) << X1-delta+epsilon , where V and W are smooth compactly supported functions, and the implied constants depend only on the associated forms and epsilon. (C) 2017 Elsevier Inc. All rights reserved.