The Density of a family of monogenic number fields

Details The Density of a family of monogenic number fields The Density of a family of monogenic number fields

2012-02-09

arxiv.org/abs/1202.2047v1

Mathematics

Number Theory

Scientific paper

A monogenic polynomial $f$ is a monic irreducible polynomial with integer coefficients which produces a monogenic number field. For a given prime $q$, using Chebotarev density theorem, we will show the density of primes $p$, such that $t^q-p$ is monogenic, is bigger or equal than $(q-1)/q$. We will also prove that, when $q=3$, the density of primes $p$, which $\mathbb{Q}(\sqrt[3]{p})$ is non-monogenic, is at least 1/9.

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