Quadratic twists of central values for GL(3)
Number Theory
2020-11-20 v2
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.
Keywords
Cite
@article{arxiv.2003.06645,
title = {Quadratic twists of central values for GL(3)},
author = {Chan Ieong Kuan and Didier Lesesvre},
journal= {arXiv preprint arXiv:2003.06645},
year = {2020}
}
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31 pages