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New zero-free regions for Dedekind zeta-functions at small and large ordinates
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abstract
Given a number field $L\neq \mathbb{Q}$, we obtain new and explicit zero-free regions for Dedekind zeta-functions of $L$, which refine the previous works of Ahn--Kwon, Kadiri, and Lee. In particular, for low-lying zeros, we extend Kadiri's result to all number fields while improving the main constant.
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An effective version of Chebotarev's density theorem
A fully explicit refinement of Lagarias and Odlyzko's effective Chebotarev theorem for all non-rational number fields, with a sharper error term for small-degree extensions.
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