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September 2017 Bounding the least prime ideal in the Chebotarev Density Theorem
Asif Zaman
Funct. Approx. Comment. Math. 57(1): 115-142 (September 2017). DOI: 10.7169/facm/1651

Abstract

Let $K$ be a number field and suppose $L/K$ is a finite Galois extension. We establish a bound for the least prime ideal occurring in the Chebotarev Density Theorem. Namely, for every conjugacy class $C$ of $\mathrm{Gal}(L/K)$, there exists a prime ideal $\mathfrak{p}$ of $K$ unramified in $L$, for which its Artin symbol $\big[ \frac{L/K}{\mathfrak{p}} \big] = C$, for which its norm $N^K_{\mathbb{Q}}\mathfrak{p}$ is a rational prime, and which satisfies \[N^K_{\mathbb{Q}} \mathfrak{p} \ll d_L^{40},\]where $d_L = |\mathrm{disc}(L/\mathbb{Q})|$. All implicit constants are effective and absolute.

Citation

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Asif Zaman. "Bounding the least prime ideal in the Chebotarev Density Theorem." Funct. Approx. Comment. Math. 57 (1) 115 - 142, September 2017. https://doi.org/10.7169/facm/1651

Information

Published: September 2017
First available in Project Euclid: 28 March 2017

zbMATH: 06864168
MathSciNet: MR3704230
Digital Object Identifier: 10.7169/facm/1651

Subjects:
Primary: 11R44
Secondary: 11M41, 11R42

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.57 • No. 1 • September 2017
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