An explicit Chebotarev density theorem under GRH

JOURNAL OF NUMBER THEORY

卷:200

Article

Grenie, Loic¹  Molteni, Giuseppe² 

[1] Univ Bergamo, Dipartimento Ingn Gestionale Informaz & Prod, Viale Marconi 5, I-24044 Dalmine, Italy

[2] Univ Milan, Dipartimento Matemat, Via Saldini 50, I-20133 Milan, Italy

关键词: Chebotarev theorem;    Generalized Riemann Hypothesis;   

DOI  :  10.1016/j.jnt.2018.12.005

来源: Elsevier

【 摘 要 】

We prove an explicit version of the Chebotarev theorem for the density of prime ideals with fixed Artin symbol, under the assumption of the validity of the Riemann hypothesis for the Dedekind zeta functions. In appendix we also give some explicit formulas counting non-trivial zeros of Hecke's L-functions, in that case without assuming the truth of the Riemann hypothesis. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free