AN EXPLICIT UPPER BOUND FOR THE LEAST PRIME IDEAL IN THE CHEBOTAREV DENSITY THEOREM
- Authors
- Ahn, Jeoung-Hwan; Kwon, Soun-Hi
- Issue Date
- 2019
- Publisher
- ANNALES INST FOURIER
- Keywords
- The Chebotarev density theorem; Dedekind zeta functions; the Deuring-Heilbronn phenomenon
- Citation
- ANNALES DE L INSTITUT FOURIER, v.69, no.3, pp.1411 - 1458
- Indexed
- SCIE
SCOPUS
- Journal Title
- ANNALES DE L INSTITUT FOURIER
- Volume
- 69
- Number
- 3
- Start Page
- 1411
- End Page
- 1458
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/68898
- DOI
- 10.5802/aif.3274
- ISSN
- 0373-0956
- Abstract
- Lagarias, Montgomery, and Odlyzko proved that there exists an effectively computable absolute constant A(1)( )such that for every finite extension K of Q, every finite Galois extension L of K with Galois group G and every conjugacy class C of G, there exists a prime ideal p of K which is unramified in L, for which [L/K/p] = C, for which N-K/Q p is a rational prime, and which satisfies N-K/Q p <= 2d(L)(A1). In this paper we show without any restriction that N-K/Q p <= d(L)(12577) if L not equal Q, using the approach developed by Lagarias, Montgomery, and Odlyzko.
- Files in This Item
- There are no files associated with this item.
- Appears in
Collections - College of Education > Department of Mathematics Education > 1. Journal Articles
Items in ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.