On the least primitive root in number fields

作     者：WANG TianZe1,& GONG Ke21School of Mathematics and Information Sciences,North China University of Water Resources and Electric Power,Zhengzhou 450011,China 2Department of Mathematics,Henan University,Kaifeng 475004,China 

作者机构：School of Mathematics and Information Sciences North China University of Water Resources and Electric Power Zhengzhou China Department of Mathematics Henan University Kaifeng China 

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

年 卷 期：2010年第53卷第9期

页      面：2489-2500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 National Natural Science Foundation of China (Grant Nos.10671056 10801105) 

主　　题：primitive root algebraic number fields Hecke zeta function 

摘      要：Let K be an algebraic number field and OK its ring of *** any prime ideal p,the group(OK/p) of the reduced residue classes of integers is *** call any element of a generator of the group(OK/p) a primitive root modulo *** both by Shoup s bound for the rational improvement and Wang and Bauer s generalization of the conditional result of Wang Yuan in 1959,we give in this paper a new bound for the least primitive root modulo a prime ideal p under the Grand Riemann Hypothesis for algebraic number *** results can be viewed as either the improvement of the result of Wang and Bauer or the generalization of the result of Shoup.