A+ CATEGORY SCIENTIFIC UNIT

PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Lower estimates for the prime ideal of degree one counting function in the Chebotarev density theorem

Volume 191 / 2019

Jeoung-Hwan Ahn, Soun-Hi Kwon Acta Arithmetica 191 (2019), 289-307 MSC: Primary 11R44, 11R42, 11M41; Secondary 11R45. DOI: 10.4064/aa180427-18-12 Published online: 20 September 2019

Abstract

Let $K$ be a number field and $L$ a finite normal extension of $K$ with Galois group $G$. For a prime ideal $\mathfrak {p}$ of $K$ which is unramified in $L$ we let $\left [\frac {L/K}{\mathfrak {p}}\right ]$ be the conjugacy class of Frobenius automorphisms corresponding to the prime ideals $\mathfrak {P}$ of $L$ lying above $\mathfrak {p}$. For a given conjugacy class $C$ of $G$ we let $\widetilde {\pi }_C (x)$ be the number of prime ideals $\mathfrak {p}$ of $K$ unramified in $L$ such that $\left [\frac {L/K}{\mathfrak {p}}\right ]=C$ and $N_{K/{\mathbb Q}}\mathfrak {p}$ is a rational prime with $N_{K/{\mathbb Q}}\mathfrak {p}\leq x$. We give some lower bounds for $\widetilde {\pi }_C (x)$.

Authors

  • Jeoung-Hwan AhnDepartment of Mathematics Education
    Korea University
    02841, Seoul, Korea
    e-mail
  • Soun-Hi KwonDepartment of Mathematics Education
    Korea University
    02841, Seoul, Korea
    e-mail

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image