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Titlebook: Cubic Fields with Geometry; Samuel A. Hambleton,Hugh C. Williams Book 2018 Springer Nature Switzerland AG 2018 binary cubic forms.cubic fi

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發(fā)表于 2025-3-21 18:19:32 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Cubic Fields with Geometry
編輯Samuel A. Hambleton,Hugh C. Williams
視頻videohttp://file.papertrans.cn/241/240708/240708.mp4
概述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 cubi
叢書名稱CMS Books in Mathematics
圖書封面Titlebook: Cubic Fields with Geometry;  Samuel A. Hambleton,Hugh C. Williams Book 2018 Springer Nature Switzerland AG 2018 binary cubic forms.cubic fi
描述The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell equation. With over 50 geometric diagrams, this book includes illustrations of many of these topics. ?The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi’s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory..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 p
出版日期Book 2018
關(guān)鍵詞binary cubic forms; cubic fields; Voronoi‘s algorithm; geometry of numbers; continued fractions; fundamen
版次1
doihttps://doi.org/10.1007/978-3-030-01404-9
isbn_ebook978-3-030-01404-9Series ISSN 1613-5237 Series E-ISSN 2197-4152
issn_series 1613-5237
copyrightSpringer Nature Switzerland AG 2018
The information of publication is updating

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Construction of All Cubic Fields of a Fixed Fundamental Discriminant (Renate Scheidler),dratic resolvent field. Berwick explained how each such quadratic integer determines the roots of a cubic polynomial with rational coefficients. He referred to these elements as (quadratic) generators since they are generators of ideals in the maximal order of the quadratic resolvent field whose cub
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,Voronoi’s Theory of Continued Fractions,field. We begin with a discussion of how Voronoi extended the idea of a simple continued fraction of a quadratic irrationality to that of a cubic irrationality. Next, we provide an account of relative minima in cubic lattices, reduced lattices (lattices in which 1 is a relative minimum), and chains
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Relative Minima Adjacent to 1 in a Reduced Lattice, a basis is essential for finding the relative minimum adjacent to 1 in a reduced lattice and a Voronoi basis for the lattice. A significant problem associated with this process is the need for working with rational approximations to cubic irrationals. We provide techniques for solving this problem
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