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Overview"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." Full Product DetailsAuthor: Tatsuo KimuraPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: No. 215 Dimensions: Width: 18.80cm , Height: 2.10cm , Length: 23.00cm Weight: 0.748kg ISBN: 9780821827673ISBN 10: 0821827677 Pages: 288 Publication Date: 30 December 2002 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsAlgebraic 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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