BELABAS, Karim; FRIEDMAN, Eduardo

doi:10.1090/S0025-5718-2014-02843-3

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BELABAS, Karim
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]

FRIEDMAN, Eduardo
Universidad de Santiago de Chile [Santiago] [USACH]

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Ce document a été publié dans

Mathematics of Computation. 2015, vol. 84, n° 291, p. 357-369

American Mathematical Society

Résumé en anglais

Assuming the Generalized Riemann Hypothesis, Bach has shown that one can calculate the residue of the Dedekind zeta function of a number field K by a clever use of the splitting of primes p < X, with an error asymptotically bounded by 8.33 log D_K/(\sqrt{X}\log X), where D_K is the absolute value of the discriminant of K. Guided by Weil's explicit formula and still assuming GRH, we make a different use of the splitting of primes and thereby improve Bach's constant to 2.33. This results in substantial speeding of one part of Buchmann's class group algorithm.< Réduire