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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 infrastructure of a global field of arbitrary unit rank
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by Felix Fontein PDF
Math. Comp. 80 (2011), 2325-2357


In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant-step operation and $f$-representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish that effective implementation of the presented methods is indeed possible, and we show how Shanks’ baby-step giant-step method can be generalized to this situation.
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Additional Information
  • Felix Fontein
  • Affiliation: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4
  • Address at time of publication: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
  • Email:
  • Received by editor(s): January 26, 2009
  • Received by editor(s) in revised form: October 7, 2010
  • Published electronically: April 26, 2011
  • Additional Notes: This work was supported in part by the Swiss National Science Foundation under grant no. 107887.
  • © Copyright 2011 Felix Fontein
  • Journal: Math. Comp. 80 (2011), 2325-2357
  • MSC (2010): Primary 11Y40; Secondary 14H05, 11R27, 11R65
  • DOI:
  • MathSciNet review: 2813364