Let ψK be the Chebyshev function of a number field K. Under the Generalized Riemann Hypothesis we prove an explicit upper bound for |ψK(x)-x| in terms of the degree and the discriminant of K. The new bound improves significantly on previous known results.
Explicit versions of the prime ideal theorem for dedekind zeta functions under GRH / L. Grenié, G. Molteni. - In: MATHEMATICS OF COMPUTATION. - ISSN 0025-5718. - 85:298(2016 Mar), pp. 889-906. [10.1090/mcom3031]
Explicit versions of the prime ideal theorem for dedekind zeta functions under GRH
G. Molteni
2016-03
Abstract
Let ψK be the Chebyshev function of a number field K. Under the Generalized Riemann Hypothesis we prove an explicit upper bound for |ψK(x)-x| in terms of the degree and the discriminant of K. The new bound improves significantly on previous known results.
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