Authors:
- Provides an up-to-date compendium of results
- Helps the reader to envision what is explained in the text
- Introduces the reader to several tools and disciplines which are applicable in the study of cubic fields
Part of the book series: CMS Books in Mathematics (CMSBM)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
About this book
The exposition includes numerous discussions on calculating with cubic fields including simple continued fractions of cubic irrational numbers, arithmetic using integer matrices, ideal class group computations, lattices over cubic fields, construction of cubic fields with a given discriminant, the search for elements of norm 1 of a cubic field with rational parametrization, and Voronoi's algorithm for finding a system of fundamental units. Throughout, the discussions are framed in terms of a binary cubic form that may be used to describe a given cubic field. This unifies the chapters of this book despite the diversity of their number theoretic topics.
Authors and Affiliations
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School of Mathematics and Physics, The University of Queensland, St. Lucia, Brisbane, Australia
Samuel A. Hambleton
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Department of Mathematics and Statistics, University of Calgary, Calgary, Canada
Hugh C. Williams
Bibliographic Information
Book Title: Cubic Fields with Geometry
Authors: Samuel A. Hambleton, Hugh C. Williams
Series Title: CMS Books in Mathematics
DOI: https://doi.org/10.1007/978-3-030-01404-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-01402-5Published: 19 November 2018
eBook ISBN: 978-3-030-01404-9Published: 07 November 2018
Series ISSN: 1613-5237
Series E-ISSN: 2197-4152
Edition Number: 1
Number of Pages: XIX, 493
Number of Illustrations: 26 b/w illustrations, 27 illustrations in colour
Topics: Algebraic Geometry, Number Theory, Algorithms