Local densities of quadratic forms and related problems

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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.