عنوان

Cubic fields with geometry /

(Number (ISBN

3030014045

(Number (ISBN

9783030014049

Erroneous ISBN

3030014029

Erroneous ISBN

9783030014025

Title Proper

Cubic fields with geometry /

General Material Designation

[Book]

First Statement of Responsibility

Samuel A. Hambleton, Hugh C. Williams.

Place of Publication, Distribution, etc.

Cham, Switzerland :

Name of Publisher, Distributor, etc.

Springer,

Date of Publication, Distribution, etc.

2018.

Specific Material Designation and Extent of Item

1 online resource (xix, 493 pages) :

Other Physical Details

illustrations (some color)

Series Title

CMS Books in Mathematics,

ISSN of Series

1613-5237

Text of Note

Includes bibliographical references and indexes.

Text of Note

Cubic fields -- Cubic ideals and lattices -- Binary cubic forms -- Construction of all cubic fields of a fixed fundamental discriminant (Renate Scheidler) -- Cubic pell equations -- The minima of forms and units by approximation -- Voronoi's theory of continued fractions -- Relative minima adjacent to 1 in a reduced lattice -- Parametrization of norm 1 elements of K.

0

Text of Note

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 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.--

Source for Acquisition/Subscription Address

Springer Nature

Stock Number

com.springer.onix.9783030014049

Title

Cubic fields with geometry.

International Standard Book Number

9783030014025

Equations, Cubic.

Geometry, Algebraic.

Algebraic Geometry.

Algorithms.

Number Theory.

Algebraic geometry.

Equations, Cubic.

Geometry, Algebraic.

MATHEMATICS-- Geometry-- General.

Number theory.

Numerical analysis.

MAT-- 012000

PBMW

PBMW

Number

Edition

Class number

Hambleton, Samuel A.

Williams, Hugh C.

Date of Transaction

20200823072940.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y