The least prime ideal in the Chebotarev density theorem

The least prime ideal in the Chebotarev density theorem

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 Turán's power sum method. Th...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2019-06, Vol.147 (6), p.2289-2303
Hauptverfasser: Kadiri, Habiba, Ng, Nathan, Wong, Peng-Jie
Format: Artikel
Sprache:eng
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Zusammenfassung: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 Turán'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 Fejér kernel.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/14384