Shifted convolution sums for GL(3)×GL(2

Abstract

For the shifted convolution sum Dh(X)=∑m=1∞λ1(1,m)λ2(m+h)V(mX), where λ1(1,m) are the Fourier coefficients of an SL(3,Z) Maass form π1, λ2(m) are those of an SL(2,Z) Maass or holomorphic form π2, and 1≤|h|≪X1+ε, we establish the bound Dh(X)≪π1,π2,εX1−1/20+ε. The bound is uniform with respect to the shift h.