Shintani zeta functions
著者
書誌事項
Shintani zeta functions
（London Mathematical Society lecture note series, 183）
Cambridge University Press, 1993
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注記
Includes bibliographical references (p. [331]-334) and index
内容説明・目次
内容説明
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. The study of the zeta functions related to prehomogeneous vector spaces can yield interesting information on the asymptotic properties of associated objects, such as field extensions and ideal classes. This is amongst the first books on this topic, and represents the author's deep study of prehomogeneous vector spaces. Here the author's aim is to generalise 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. This book will be of great interest to all serious workers in analytic number theory.
目次
- Introduction
- 1. The general theory
- 2. Eisenstein series
- 3. The general program
- 4. The zeta function for the spaces
- 5. The case G=GL(2)YGL(2), V=Sym2 k2fk2
- 6. The case G=GL(2)YGL(1)2, V=Sym2 k2fk
- 7. The case G=GL(2)YGL(1), V=Sym2 k2fk2
- 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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