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arXiv · 1704.03451

The least unramified prime which does not split completely

Asif Zaman
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Abstract

Let $K/F$ be a finite extension of number fields of degree $n \geq 2$. We establish effective field-uniform unconditional upper bounds for the least norm of a prime ideal of $F$ which is degree 1 over $\mathbb{Q}$ and does not ramify or split completely in $K$. We improve upon the previous best known general estimates due to X. Li when $F = \mathbb{Q}$ and Murty-Patankar when $K/F$ is Galois. Our bounds are the first when $K/F$ is not assumed to be Galois and $F \neq \mathbb{Q}$.

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Asif Zaman. 2017-04-11. The least unramified prime which does not split completely. https://doi.org/10.1112/s0025579318000190

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