Sums of multiplicative coefficients twisted by Frobenius traces.

Let a E (n) be the normalized Frobenius traces. For any multiplicative function f satisfying some mild conditions, we investigate the sum ∑ n = 1 N f (n) a E (n) and obtain a nontrivial bound. We also prove cancelation in the sum of Frobenius traces twisted by the coefficients of automorphic L-function on GLm. [ABSTRACT FROM AUTHOR]