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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields
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by Stéphane R. Louboutin PDF
Math. Comp. 80 (2011), 1813-1822 Request permission


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:
  • Received by editor(s): November 25, 2009
  • Received by editor(s) in revised form: June 15, 2010
  • Published electronically: January 25, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 80 (2011), 1813-1822
  • MSC (2010): Primary 11R42; Secondary 11R16, 11R29
  • DOI:
  • MathSciNet review: 2785481