Buch, Englisch, 493 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 934 g
Reihe: CMS Books in Mathematics
Buch, Englisch, 493 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 934 g
Reihe: CMS Books in Mathematics
ISBN: 978-3-030-01402-5
Verlag: Springer International Publishing
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.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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.