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arXiv · 1305.0035

Computing the residue of the Dedekind zeta function

Karim Belabas·Eduardo Friedman
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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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Karim Belabas, Eduardo Friedman. 2013-04-30. Computing the residue of the Dedekind zeta function. https://arxiv.org/abs/1305.0035

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