Abstract
Let [Formula: see text] be a self-contragredient irreducible unitary cuspidal representation of [Formula: see text] with [Formula: see text], and [Formula: see text] be the automorphic [Formula: see text]-function attached to [Formula: see text]. Assume that [Formula: see text] is self-contragredient. Under the Generalized Ramanujan Conjecture and Generalized Riemann Hypothesis for [Formula: see text], the estimate [Formula: see text] holds for all real number [Formula: see text] as [Formula: see text].
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