Fractional moments of automorphic L-functions on GL(m)

Abstract

Let π be an irreducible unitary cuspidal representation of \(GL_m \left( {\mathbb{A}_\mathbb{Q} } \right)\), m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-function L(s, π) on the critical line under Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the truth of Generalized Riemann Hypothesis.