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arXiv · 2003.06645

Quadratic twists of central values for GL(3)

Chan Ieong Kuan·Didier Lesesvre
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Abstract

We prove that a cuspidal automorphic representation of GL(3) over any number field is determined by the quadratic twists of its central value. In the case of a non-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 the field of rational numbers and explored only for Gelbart-Jacquet lifts.

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Chan Ieong Kuan, Didier Lesesvre. 2020-03-14. Quadratic twists of central values for GL(3). https://arxiv.org/abs/2003.06645

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