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Mosc. Math. J., 2015, Volume 15, Number 4, Pages 727–740 (Mi mmj583)  

Explicit upper bounds for residues of Dedekind zeta functions

Stéphane R. Louboutin

Institut de Mathématiques de Marseille, Aix Marseille Université, 163 Avenue de Luminy, Case 907, 13288 Marseille Cedex 9, FRANCE

Abstract: Explicit bounds on the residues at $s=1$ of the Dedekind zeta-functions of number fields (in terms of their degree and of the logarithm of the absolute value of their discriminant) have long been known. They date back to C. L. Siegel and E. Landau. The author gave a neat explicit bound in 2000, the best known bound until recently. In 2012 X. Li improved upon this bound. His results, although effective, were not explicit. Here we make one of his two bounds explicit and determine when it is the best known one.

Key words and phrases: Dedekind zeta functions, residues, Stechkin lemma.

DOI: https://doi.org/10.17323/1609-4514-2015-15-4-727-740

Full text: http://www.mathjournals.org/.../2015-015-004-009.html
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Bibliographic databases:

MSC: Primary 11R42; Secondary 11R29
Received: January 30, 2015; in revised form August 25, 2015
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Citation: Stéphane R. Louboutin, “Explicit upper bounds for residues of Dedekind zeta functions”, Mosc. Math. J., 15:4 (2015), 727–740

Citation in format AMSBIB
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\by St\'ephane~R.~Louboutin
\paper Explicit upper bounds for residues of Dedekind zeta functions
\jour Mosc. Math.~J.
\yr 2015
\vol 15
\issue 4
\pages 727--740
\mathnet{http://mi.mathnet.ru/mmj583}
\crossref{https://doi.org/10.17323/1609-4514-2015-15-4-727-740}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3438830}
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