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The theory of prehomogeneous vector spaces is a relatively new subject although its origin can be traced back through the works of Siegel to Gauss. This is the first book on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalize Shintani's approach from the viewpoint of geometric invariant theory, and in some special cases he also determines not only the pole structure but also the principal part of the zeta function.Read more
- Only comprehensive book on this subject
- Author is the prime mover behind the development of the subject
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- Date Published: February 1994
- format: Paperback
- isbn: 9780521448048
- length: 352 pages
- dimensions: 228 x 152 x 20 mm
- weight: 0.507kg
- availability: Available
Table of Contents
1. The general theory
2. Eisenstein series
3. The general program
4. The zeta function for the spaces
5. The case G=GL(2)¥GL(2), V=Sym2 k2ƒk2
6. The case G=GL(2)¥GL(1)2, V=Sym2 k2ƒk
7. The case G=GL(2)¥GL(1), V=Sym2 k2ƒk2
8. Invariant theory of pairs of ternary quadratic forms
9. Preliminary estimates
10. The non-constant terms associated with unstable strata
11. Unstable distributions
12. Contributions from unstable strata
13. The main theorem.
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