عنوان

Cubic fields with geometry /

شابک

3030014045

شابک

9783030014049

شابک اشتباه

3030014029

شابک اشتباه

9783030014025

عنوان اصلي

Cubic fields with geometry /

نام عام مواد

[Book]

نام نخستين پديدآور

Samuel A. Hambleton, Hugh C. Williams.

محل نشرو پخش و غیره

Cham, Switzerland :

نام ناشر، پخش کننده و غيره

Springer,

تاریخ نشرو بخش و غیره

2018.

نام خاص و کميت اثر

1 online resource (xix, 493 pages) :

ساير جزييات

illustrations (some color)

عنوان فروست

CMS Books in Mathematics,

شاپا ي ISSN فروست

1613-5237

متن يادداشت

Includes bibliographical references and indexes.

متن يادداشت

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.

بدون عنوان

0

متن يادداشت

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.--

منبع سفارش / آدرس اشتراک

Springer Nature

شماره انبار

com.springer.onix.9783030014049

عنوان

Cubic fields with geometry.

شماره استاندارد بين المللي کتاب و موسيقي

9783030014025

موضوع مستند نشده

Equations, Cubic.

موضوع مستند نشده

Geometry, Algebraic.

موضوع مستند نشده

Algebraic Geometry.

موضوع مستند نشده

Algorithms.

موضوع مستند نشده

Number Theory.

موضوع مستند نشده

Algebraic geometry.

موضوع مستند نشده

Equations, Cubic.

موضوع مستند نشده

Geometry, Algebraic.

موضوع مستند نشده

MATHEMATICS-- Geometry-- General.

موضوع مستند نشده

Number theory.

موضوع مستند نشده

Numerical analysis.

موضوع مستند نشده

MAT-- 012000

موضوع مستند نشده

PBMW

موضوع مستند نشده

PBMW

شماره

ويراست

شماره رده

مستند نام اشخاص تاييد نشده

Hambleton, Samuel A.

مستند نام اشخاص تاييد نشده

Williams, Hugh C.

تاريخ عمليات

20200823072940.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y