Abstract
Abstract We prove that a cuspidal automorphic representation of $\mathrm{GL}(3)$ over any number field is determined by the quadratic twists of its central value. In the case π is not a Gelbart–Jacquet lift, the result is conditional on the analytic behavior of a certain Euler product. We deduce the nonvanishing of infinitely many quadratic twists of central values. This generalizes a result of Chinta and Diaconu that was valid only over Q and explored only for Gelbart–Jacquet lifts.
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