Shifted convolution sums of GL(m) cusp forms with Θ-series

Let lambda(pi) (1, ..., 1, n) be the normalized Fourier coefficients of an even Hecke-Maass form pi for SL(m, Z) with m >= 3, and r(3)(n) = #{(n(1), n(2), n(3)) is an element of Z(3) : n = n(1)(2) + n(2)(2) + n(3)(2)}. In this paper, we introduce a refined version of the circle method to derive a sharp bound for the shifted convolution sum of GL(m) Fourier coefficients lambda(pi)(1, ..., 1, n) and r(3)(n), which improves previous results (even under the generalized Ramanujan conjecture).