2011 Fiscal Year Final Research Report
Number theory for parabolic type prehomogeneous vector spaces and their associated zeta functions
| Project/Area Number |
20740018
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Single-year Grants |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kobe University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | 整数論 / 密度定理 / ゼータ関数 |
|---|
| Research Abstract |
(1) I classified the integral models for the space of binary cubic forms, and proved that the associated zeta functions all satisfy the dual identities(joint work with Y. Ohno and S. Wakatsuki).
(2) I determined the second main for counting cubic fields and therefore solved the Roberts' conjecture. Moreover, by introducing the notion of orbital L functions, I showed that there are biases for counting cubic fields in arithmetic progressions(joint work with F. Thorne).
(3) In an ongoing work, I am studying one particular reducible prehomogeneous vector space of ten dimensional. I gave an algebraic interpretation of integer orbits, and also find that the associated zeta function in two variables are expressed in terms of a family of zeta functions for the space of binary cubic forms with level structures(joint work with G. Chinta).
|
