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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Contributor : Karim Belabas <>
Submitted on : Tuesday, December 10, 2013 - 3:10:09 PM
Last modification on : Thursday, January 11, 2018 - 6:22:36 AM

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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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