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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2024 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Algorithms in algebraic number theory
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by H. W. Lenstra PDF
Bull. Amer. Math. Soc. 26 (1992), 211-244 Request permission

Abstract:

In this paper we discuss the basic problems of algorithmic algebraic number theory. The emphasis is on aspects that are of interest from a purely mathematical point of view, and practical issues are largely disregarded. We describe what has been done and, more importantly, what remains to be done in the area. We hope to show that the study of algorithms not only increases our understanding of algebraic number fields but also stimulates our curiosity about them. The discussion is concentrated of three topics: the determination of Galois groups, the determination of the ring of integers of an algebraic number field, and the computation of the group of units and the class group of that ring of integers.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 26 (1992), 211-244
  • MSC (2000): Primary 11Y40; Secondary 11R27, 11R29
  • DOI: https://doi.org/10.1090/S0273-0979-1992-00284-7
  • MathSciNet review: 1129315