ON EXPONENTIAL SUMS INVOLVING COEFFICIENTS OF L-FUNCTIONS FOR SL(3, Z) OVER PRIMES.

Let L(s, F) be the L-function associated with a Hecke-Maass form F for SL(3, Z), with AF(n, 1) denoting the nth coefficient of the Dirichlet series for it. It is proved that, for N ≥ 2 and any α ∈ R, there exists an effective constant c > 0 such that ∑n≤N ∧(n)AF(n, 1)e(nα) ≪ N exp(-c √ log N), where ∧(n) is the von Mangoldt function, and the implied constant depends only on F. [ABSTRACT FROM AUTHOR]