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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The Euclidean algorithm in quintic and septic cyclic fields
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by Pierre Lezowski and Kevin J. McGown PDF
Math. Comp. 86 (2017), 2535-2549 Request permission


Conditionally on the Generalized Riemann Hypothesis (GRH), we prove the following results: (1) a cyclic number field of degree $5$ is norm-Euclidean if and only if $\Delta =11^4,31^4,41^4$; (2) a cyclic number field of degree $7$ is norm-Euclidean if and only if $\Delta =29^6,43^6$; (3) there are no norm-Euclidean cyclic number fields of degrees $19$, $31$, $37$, $43$, $47$, $59$, $67$, $71$, $73$, $79$, $97$.

Our proofs contain a large computational component, including the calculation of the Euclidean minimum in some cases; the correctness of these calculations does not depend upon the GRH. Finally, we improve on what is known unconditionally in the cubic case by showing that any norm-Euclidean cyclic cubic field must have conductor $f\leq 157$ except possibly when $f\in (2\cdot 10^{14}, 10^{50})$.

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Additional Information
  • Pierre Lezowski
  • Affiliation: Université Blaise Pascal, Laboratoire de Mathématiques UMR 6620, Campus Universitaire des Cézeaux, BP 80026, 63171 Aubière Cédex, France
  • MR Author ID: 988126
  • Email:
  • Kevin J. McGown
  • Affiliation: California State University, Chico, Department of Mathematics and Statistics, 601 E. Main St., Chico, California 95929
  • MR Author ID: 768800
  • ORCID: 0000-0002-5925-801X
  • Email:
  • Received by editor(s): December 1, 2015
  • Received by editor(s) in revised form: March 26, 2016
  • Published electronically: February 16, 2017
  • © Copyright 2017 American Mathematical Society
  • Journal: Math. Comp. 86 (2017), 2535-2549
  • MSC (2010): Primary 11A05, 11R04, 11Y40; Secondary 11R16, 11R80, 11L40, 11R32
  • DOI:
  • MathSciNet review: 3647971