Shintani Zeta Functions

ISBN-13: 9780521448048 / Angielski / Miękka / 1994 / 352 str.

Akihiko Yukie

Opis

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.

Spis treści

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)¥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.