A supplement to Chebotarev's density theorem

作     者：Gergely Harcos Kannan Soundararajan Gergely Harcos;Kannan Soundararajan

作者机构：Alfréd Rényi Institute of MathematicsBudapest 1364Hungary Department of MathematicsStanford UniversityStanfordCA 94305USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第12期

页      面：2749-2753页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

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 

主　　题：Chebotarev's density theorem Artin L-functions Heilbronn characters 

摘      要：Let L/K be a Galois extension of number fields with Galois group *** 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 *** deduce this by relating the poles of the corresponding Dirichlet series to the zeros ofζ_L(s)/ζ_K(s).