Explicit smoothed prime ideals theorems under GRH
نویسندگان
چکیده
Let ψK be the Chebyshev function of a number field K. Let ψ K (x) := ∫ x 0 ψK(t) dt and ψ (2) K (x) := 2 ∫ x 0 ψ (1) K (t) dt. We prove under GRH (Generalized Riemann Hypothesis) explicit inequalities for the differences |ψ K (x) − x 2 | and |ψ K (x) − x 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. Math. Comp. 85(300), 1875–1899 (2016). Electronically published on October 6, 2015. DOI: http://dx.doi.org/10.1090/mcom3039
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ورودعنوان ژورنال:
- Math. Comput.
دوره 85 شماره
صفحات -
تاریخ انتشار 2016