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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields


Author: Stéphane R. Louboutin
Journal: Math. Comp. 80 (2011), 1813-1822
MSC (2010): Primary 11R42; Secondary 11R16, 11R29
Published electronically: January 25, 2011
MathSciNet review: 2785481
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Abstract: Let $ K$ be an algebraic number field. Assume that $ \zeta_K(s)/\zeta (s)$ is entire. We give an explicit upper bound for the residue at $ s=1$ of the Dedekind zeta function $ \zeta_K(s)$ of $ K$. We deduce explicit upper bounds on class numbers of cubic and quartic number fields.


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Additional Information

Stéphane R. Louboutin
Affiliation: Institut de Mathématiques de Luminy, UMR 6206, 163, avenue de Luminy, Case 907, 13288 Marseille Cedex 9, France
Email: loubouti@iml.univ-mrs.fr

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02457-9
PII: S 0025-5718(2011)02457-9
Keywords: Dedekind zeta function, number field, class number
Received by editor(s): November 25, 2009
Received by editor(s) in revised form: June 15, 2010
Published electronically: January 25, 2011
Article copyright: © Copyright 2011 American Mathematical Society