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

Let λ π (1 , ... , 1 , n) be the normalized Fourier coefficients of an even Hecke–Maass form π for S L (m , Z) with m ≥ 3 , and r 3 (n) = # { (n 1 , n 2 , n 3) ∈ 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 λ π (1 , ... , 1 , n) and r 3 (n) , which improves previous results (even under the generalized Ramanujan conjecture). [ABSTRACT FROM AUTHOR]