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.
(2019). An explicit Chebotarev density theorem under GRH [journal article - articolo]. In JOURNAL OF NUMBER THEORY. Retrieved from http://hdl.handle.net/10446/140232
An explicit Chebotarev density theorem under GRH
Grenié, Loïc;
2019-01-01
Abstract
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.File allegato/i alla scheda:
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