The least prime ideal in the Chebotarev density theorem
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- by Habiba Kadiri, Nathan Ng and Peng-Jie Wong PDF
- Proc. Amer. Math. Soc. 147 (2019), 2289-2303
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 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.References
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Additional Information
- Habiba Kadiri
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 Canada
- MR Author ID: 760548
- Email: habiba.kadiri@uleth.ca
- Nathan Ng
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 Canada
- MR Author ID: 721483
- Email: nathan.ng@uleth.ca
- Peng-Jie Wong
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, 4401 University Drive, Lethbridge, Alberta, T1K 3M4 Canada
- MR Author ID: 1211484
- Email: pengjie.wong@uleth.ca
- Received by editor(s): July 14, 2018
- Received by editor(s) in revised form: September 5, 2018
- Published electronically: February 14, 2019
- Additional Notes: This research was partially supported by the NSERC Discovery grants of the first and second author.
The third author was supported by a PIMS postdoctoral fellowship and the University of Lethbridge. - Communicated by: Amanda Folsom
- © Copyright 2019 Habiba Kadiri, Nathan Ng, and Peng-Jie Wong
- Journal: Proc. Amer. Math. Soc. 147 (2019), 2289-2303
- MSC (2010): Primary 11R44; Secondary 11R42, 11M41, 11Y35
- DOI: https://doi.org/10.1090/proc/14384
- MathSciNet review: 3951412