| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| 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).
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