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.
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Mathematics of Computation, American Mathematical Society, 2015, 84, pp.357-369
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Contributeur : Karim Belabas <>
Soumis le : mardi 10 décembre 2013 - 15:10:09
Dernière modification le : jeudi 11 janvier 2018 - 06:22:36

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  • HAL Id : hal-00916654, version 1
  • ARXIV : 1305.0035

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Karim Belabas, Eduardo Friedman. Computing the residue of the Dedekind zeta function. Mathematics of Computation, American Mathematical Society, 2015, 84, pp.357-369. 〈hal-00916654〉

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