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Journal Articles Mathematics of Computation Year : 2015

Computing the residue of the Dedekind zeta function

Abstract

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.

Dates and versions

hal-00916654 , version 1 (10-12-2013)

Identifiers

Cite

Karim Belabas, Eduardo Friedman. Computing the residue of the Dedekind zeta function. Mathematics of Computation, 2015, 84 (291), pp.357-369. ⟨10.1090/S0025-5718-2014-02843-3⟩. ⟨hal-00916654⟩
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