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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.


Constructing abelian extensions with prescribed norms
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by Christopher Frei and Rodolphe Richard HTML | PDF
Math. Comp. 91 (2022), 381-399 Request permission


Given a number field $K$, a finite abelian group $G$ and finitely many elements $\alpha _1,\ldots ,\alpha _t\in K$, we construct abelian extensions $L/K$ with Galois group $G$ that realise all of the elements $\alpha _1,\ldots ,\alpha _t$ as norms of elements in $L$. In particular, this shows existence of such extensions for any given parameters.

Our approach relies on class field theory and a recent formulation of Tate’s characterisation of the Hasse norm principle, a local-global principle for norms. The constructions are sufficiently explicit to be implemented on a computer, and we illustrate them with concrete examples.

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Additional Information
  • Christopher Frei
  • Affiliation: TU Graz, Institute of Analysis and Number Theory, Steyrergasse 30/II, 8010 Graz, Austria
  • MR Author ID: 938397
  • ORCID: 0000-0001-8962-9240
  • Email:
  • Rodolphe Richard
  • Affiliation: 13, rue du Croisic, 22200 Plouisy, Bretagne, France
  • Address at time of publication: University College London, 25 Gordon Street, WC1H 0AY London, United Kingdom
  • MR Author ID: 875874
  • Email:
  • Received by editor(s): July 2, 2020
  • Received by editor(s) in revised form: December 14, 2020, and April 8, 2021
  • Published electronically: July 22, 2021
  • Additional Notes: The first author was supported by EPSRC grant EP/T01170X/1. The second author was supported by ERC grant GeTeMo 617129, and Leverhulme Research Project Grant “Diophantine problems related to Shimura varieties”
  • © Copyright 2021 American Mathematical Society
  • Journal: Math. Comp. 91 (2022), 381-399
  • MSC (2020): Primary 11Y40, 11R37; Secondary 14G05, 11D57
  • DOI:
  • MathSciNet review: 4350543