Introduction to Prehomogeneous Vector Spaces
2002
American Mathematical Society (Verlag)
978-0-8218-2767-3 (ISBN)
American Mathematical Society (Verlag)
978-0-8218-2767-3 (ISBN)
- Titel z.Zt. nicht lieferbar
- Versandkostenfrei
- Auch auf Rechnung
- Artikel merken
Explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces, and a classification theory of irreducible prehomogeneous vector spaces.
This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. The subject combines elements of several areas of mathematics, such as algebraic geometry, Lie groups, analysis, number theory, and invariant theory. An important objective is to create applications to number theory. For example, one of the key topics is that of zeta functions attached to prehomogeneous vector spaces; these are generalizations of the Riemann zeta function, a cornerstone of analytic number theory.Prehomogeneous vector spaces are also of use in representation theory, algebraic geometry and invariant theory. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces, and a classification theory of irreducible prehomogeneous vector spaces. It strives, and to a large extent succeeds, in making this content, which is by its nature fairly technical, self-contained and accessible. The first section of the book, 'Overview of the theory and contents of this book', is particularly noteworthy as an excellent introduction to the subject.
This is the first introductory book on the theory of prehomogeneous vector spaces, introduced in the 1970s by Mikio Sato. The author was an early and important developer of the theory and continues to be active in the field. The subject combines elements of several areas of mathematics, such as algebraic geometry, Lie groups, analysis, number theory, and invariant theory. An important objective is to create applications to number theory. For example, one of the key topics is that of zeta functions attached to prehomogeneous vector spaces; these are generalizations of the Riemann zeta function, a cornerstone of analytic number theory.Prehomogeneous vector spaces are also of use in representation theory, algebraic geometry and invariant theory. This book explains the basic concepts of prehomogeneous vector spaces, the fundamental theorem, the zeta functions associated with prehomogeneous vector spaces, and a classification theory of irreducible prehomogeneous vector spaces. It strives, and to a large extent succeeds, in making this content, which is by its nature fairly technical, self-contained and accessible. The first section of the book, 'Overview of the theory and contents of this book', is particularly noteworthy as an excellent introduction to the subject.
Algebraic preliminaries Relative invariants of prehomogeneous vector spaces Analytic preliminaries The fundamental theorem of prehomogeneous vector spaces The zeta functions of prehomogeneous vector spaces Convergence of zeta functions of prehomogeneous vector spaces Classification of prehomogeneous vector spaces Appendix: Table of irreducible reduced prehomogeneous vector spaces Bibliography Index of symbols Index.
| Erscheint lt. Verlag | 1.2.2003 |
|---|---|
| Reihe/Serie | Translations of Mathematical Monographs |
| Zusatzinfo | bibliography, index |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 748 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-8218-2767-7 / 0821827677 |
| ISBN-13 | 978-0-8218-2767-3 / 9780821827673 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Eine Einführung für Studienanfänger
Buch | Softcover (2025)
Springer Spektrum (Verlag)
CHF 41,95
Sieben ausgewählte Themenstellungen
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 89,95
