By Tatsuo Kimura
This is often the 1st introductory e-book at the conception of prehomogeneous vector areas, brought within the Nineteen Seventies through Mikio Sato. the writer used to be an early and demanding developer of the idea and remains to be energetic within the box. the topic combines components of a number of parts of arithmetic, similar to algebraic geometry, Lie teams, research, quantity conception, and invariant thought. a huge goal is to create purposes to quantity thought. for instance, one of many key themes is that of zeta services hooked up to prehomogeneous vector areas; those are generalizations of the Riemann zeta functionality, a cornerstone of analytic quantity conception. Prehomogeneous vector areas also are of use in illustration concept, algebraic geometry and invariant idea. This ebook explains the elemental ideas of prehomogeneous vector areas, the basic theorem, the zeta features linked to prehomogeneous vector areas, and a type concept of irreducible prehomogeneous vector areas. It strives, and to a wide quantity succeeds, in making this content material, that's through its nature quite technical, self-contained and available. the 1st component to the publication, ""Overview of the idea and contents of this book,"" is very noteworthy as an exceptional creation to the topic.
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