Let ψK be the Chebyshev function of a number field K. Let ψK(1)(x) :=∫0xψK(t) dt and ψK(2)(x) :=2∫0xψK(1)(t) dt. We prove under GRH (Generalized Riemann Hypothesis) explicit inequalities for the differences |ψK(1) (x)-x2/2| and |ψK(2) (x)-x3/3|. We deduce an efficient algorithm for the computation of the residue of the Dedekind zeta function and a bound on small-norm prime ideals.
Explicit smoothed prime ideals theorems under GRH / L. Grenié, G. Molteni. - In: MATHEMATICS OF COMPUTATION. - ISSN 0025-5718. - 85:300(2016 Jul), pp. 1875-1899. [10.1090/mcom3039]
Explicit smoothed prime ideals theorems under GRH
G. MolteniUltimo
2016
Abstract
Let ψK be the Chebyshev function of a number field K. Let ψK(1)(x) :=∫0xψK(t) dt and ψK(2)(x) :=2∫0xψK(1)(t) dt. We prove under GRH (Generalized Riemann Hypothesis) explicit inequalities for the differences |ψK(1) (x)-x2/2| and |ψK(2) (x)-x3/3|. We deduce an efficient algorithm for the computation of the residue of the Dedekind zeta function and a bound on small-norm prime ideals.
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