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arXiv · 1902.08640

The least prime ideal in the Chebotarev Density Theorem

Habiba Kadiri·Nathan Ng·Peng-Jie Wong
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Abstract

In this article, we prove a new bound for the least prime ideal in the Chebotarev density theorem, which improves the main theorem of Zaman [Funct. Approx. Comment. Math. 57 (2017), no.1, 115-142] by a factor of $5/2$. Our main improvement comes from a new version of Tur\'an's power sum method. The key new idea is to use Harnack's inequality for harmonic functions to derive a superior lower bound for the generalised Fej\'er kernel.

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Habiba Kadiri, Nathan Ng, Peng-Jie Wong. 2019-02-22. The least prime ideal in the Chebotarev Density Theorem. https://arxiv.org/abs/1902.08640

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