A supplement to Chebotarev's density theorem  

作　　者：Gergely Harcos Kannan Soundararajan 

机构地区：[1]Alfréd Rényi Institute of Mathematics,Budapest 1364,Hungary [2]Department of Mathematics,Stanford University,Stanford,CA 94305,USA

出　　处：《Science China Mathematics》2023年第12期2749-2753,共5页中国科学：数学（英文版）

基　　金：supported by the Rényi Intézet Lendület Automorphic Research Group and NKFIH(National Research,Development and Innovation Office)(Grant No.K 143876);supported in part by a grant from the National Science Foundation;a Simons Investigator Award from the Simons Foundation。

摘　　要：Let L/K be a Galois extension of number fields with Galois group G.We show that if the density of prime ideals in K that split totally in L tends to 1/|G|with a power saving error term,then the density of prime ideals in K whose Frobenius is a given conjugacy class C■G tends to|C|/|G|with the same power saving error term.We deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζ_L(s)/ζ_K(s).

关 键 词：Chebotarev's density theorem Artin L-functions Heilbronn characters 

分 类 号：O156[理学—数学]