1995 Fiscal Year Final Research Report Summary
Local densities of quadratic forms and related problems
| Project/Area Number |
06640003
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Muroran Institute of Technology |
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Principal Investigator |
KATSURADA Hidenori Muroran Institute of Technology, 工学部, 教授 (80133792)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEGAHARA Yugen Muroran Institute of Technology, 工学部, 助教授 (10211351)
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| Project Period (FY) |
1994 – 1995
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| Keywords | Local densities / Siegel-Eisenstein series / Maass zeta function |
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| Research Abstract |
In this research, we found a recursion formula for local densitires, which is useful to give an explicit formula for local desities. Further applying this to Sigel-Eisenstein series, we gave several important results about the Fourier coefficients of Siegel-Eisenstein series.
First, we gave a precise information about the denominator of a power series of one variables defined by Y.Kitaoka.
Secondly, we gave an explicit formula for the Fourier coefficients of Siegel-Eisenstein series of degree 3.
Thirdly, we gave an explicit formula for Koecher-Maass Dirichlet series associated with Siegel-Eisenstein series. This is a joint work with T.Ibukiyama.
Finally we gave a precise information about the denominaotor and numerator of a power series of several variables attached to local densities of quadratic forms.
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