First moments of Fourier coefficients of GL(r) cusp forms

Let π   be an irreducible cuspidal automorphic representation of GL(r,A)GL(r,A) where r≥2r≥2 and AA is the adele ring of QQ. Let aπ(n)aπ(n) denote the nth Dirichlet series coefficient of the L-function associated to π  . The main goal of this paper is to obtain strong bounds for the first moment ∑n≤xaπ(n)∑n≤xaπ(n) as x→∞x→∞. The bounds we obtain are better than all previously obtained bounds for the higher rank situation when r≥3r≥3 and π   is not a symmetric power of a GL(2,A)GL(2,A) cuspidal automorphic representation.