Lower Bounds for the Least Prime in Chebotarev

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.

References in corpus (1)

• Bounding the least prime ideal in the Chebotarev Density Theorem

Cited by in corpus (2)

• Distribution of Frobenius elements in families of Galois extensions
• Polynomials over Ring of Integers of Global Fields that have Roots Modulo Every Finite Indexed Subgroup