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.

An explicit Chebotarev density theorem under GRH / L. Grenié, G. Molteni. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 200:(2019), pp. 441-485. [10.1016/j.jnt.2018.12.005]

An explicit Chebotarev density theorem under GRH

G. Molteni
2019

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.
Chebotarev theorem; Generalized Riemann Hypothesis; Algebra and Number Theory
Settore MAT/05 - Analisi Matematica
Settore MAT/02 - Algebra
2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/634041
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