English

Lower Bounds for the Least Prime in Chebotarev

Number Theory 2019-12-11 v4

Abstract

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

Keywords

Cite

@article{arxiv.1810.09566,
  title  = {Lower Bounds for the Least Prime in Chebotarev},
  author = {Andrew Fiori},
  journal= {arXiv preprint arXiv:1810.09566},
  year   = {2019}
}