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Lower Bounds for the Least Prime in Chebotarev

Published 22 Oct 2018 in math.NT | (1810.09566v4)

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

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Authors (1)

  1. Andrew Fiori 

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