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Non-vanishing for cubic Hecke $L$-functions
Let $ω$ be a primitive cubic root of unity. We study the non-vanishing problem for the family of Hecke $L$-functions associated to primitive cubic characters defined over the Eisenstein quadratic number field $\mathbb{Q}(ω)$. We prove unconditionally that a positive proportion of Hecke $L$-functions
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