Cubic Fields with Geometry

• Main Authors: Hambleton, Samuel A. (Author, http://id.loc.gov/vocabulary/relators/aut), Williams, Hugh C. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: CMS Books in Mathematics, Ouvrages de mathématiques de la SMC,
• Subjects: Algebraic geometry.; Number theory.; Algorithms.; Algebraic Geometry.; Number Theory.

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 equ...

Table of Contents:

• Chapter 1- Cubic fields
• Chapter 2- Cubic ideals and lattices
• Chapter 3- Binary cubic forms
• Chapter 4- Construction of all cubic fields of a fixed fundamental discriminant (Renate Scheidler)
• Chapter 5- Cubic Pell equations
• Chapter 6- The minima of forms and units by approximation
• Chapter 7- Voronoi's theory of continued fractions
• Chapter 8- Relative minima adjacent to 1 in a reduced lattice
• Chapter 9- Parametrization of norm 1 elements of K
• Tables and References
• Author Index
• Symbol Index
• General Index.