The spectral decomposition of shifted convolution sums over number fields
Let p1, p2 be cuspidal automorphic representations of GL2 over a number field F with Hecke eigenvalues lp1(m),lp2(m) For nonzero integers l1,l2F and compactly supported functions W1,W2 on Fx, a spectral decomposition of the shifted convolution sum l1t1 l2t2=q0t1,t2nlp1(t1n 1)lp2(t2n 1) N(t1t2n 2)W1(l1t1)W2(l2t2) is obtained for any nonzero fractional ideal n and any nonzero element qn.