#### 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 $ℚ$, for which the smallest prime $p$ of $ℚ$ which splits completely in $L$ has size at least ${\left(log\left(|{D}_{L}|\right)\right)}^{2+o\left(1\right)}$. This gives a converse to various upper bounds, which shows that they are best possible.

##### Keywords
Chebotarev, class groups
Primary: 11R44
Secondary: 11R29