Moscow Mathematical Journal
Volume 15, Issue 4, October–December 2015 pp. 727–740.
Explicit Upper Bounds for Residues of Dedekind Zeta Functions
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. 2010 Math. Subj. Class. Primary: 11R42; Secondary: 11R29.
Authors:
Stéphane R. Louboutin
Author institution:Institut de Mathématiques de Marseille, Aix Marseille Université, 163 Avenue de Luminy, Case 907, 13288 Marseille Cedex 9, FRANCE
Summary:
Keywords: Dedekind zeta functions, residues, Stechkin lemma.
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