Vol. 13, No. 9, 2019

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Lower bounds for the least prime in Chebotarev

Andrew Fiori

Vol. 13 (2019), No. 9, 2199–2203
Abstract

In this paper we show there exists an infinite family of number fields L, Galois over , for which the smallest prime p of which splits completely in L has size at least (log(|DL|))2+o(1). This gives a converse to various upper bounds, which shows that they are best possible.

Keywords
Chebotarev, class groups
Mathematical Subject Classification 2010
Primary: 11R44
Secondary: 11R29
Milestones
Received: 1 March 2019
Revised: 8 May 2019
Accepted: 27 June 2019
Published: 7 December 2019
Authors
Andrew Fiori
Department of Mathematics and Computer Science
University of Lethbridge
AB
Canada