A new bound on the relative error in the Chebotarev density theorem

Jesse Thorner; Zhuo Zhang

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arXiv · 2412.01802

A new bound on the relative error in the Chebotarev density theorem

Jesse Thorner·Zhuo Zhang

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Abstract

We unconditionally improve the uniformity in the Chebotarev density theorem for Galois extensions of number fields using nonabelian base change. This leads to the first theoretical improvement over Weiss's bound for the least norm of an unramified prime ideal with given Artin symbol.

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Jesse Thorner, Zhuo Zhang. 2024-12-02. A new bound on the relative error in the Chebotarev density theorem. https://arxiv.org/abs/2412.01802

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