| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
|---|
| Outline of Final Research Achievements |
First we generalized Zagier’s reciprocity for higer-dimensional Dedekind sum to the case where the given integers satisfy weaker conditions. Our method is geometrical in the sense that the comparison of the invariants of several cyclic quotient singularities induce the reciprocity. The main tool of the proof is the orbifold signature theorem with non-isolated fixed points locus.
Second, we extended Myerson-Holzapfel formula which expresses the classical Dedekind sum by means of continued fraction as follows: We define the notion of higher-dimensional continued fraction whose algorithm corresponds to the toric resolution process of Fujiki-Oka for cyclic quotient singularities. Then we expressed the three-dimensional Fourier-Dedekind sum with weight zero by means of this continued fraction. As a tool of the proof, we slightly extend the observation of Pommersheim for the Chow ring of simplicial toric varieties.
|
