  We give a formula for certain values and derivatives of Siegel series and use
them to compute Fourier coefficients of derivatives of the Siegel Eisenstein
series of weight g/2 and genus g. When g=4, the Fourier coefficient is
approximated by a certain Fourier coefficient of the central derivative of the
Siegel Eisenstein series of weight 2 and genus 3, which is related to the
intersection of 3 arithmetic modular correspondences. Applications include a
relation between weighted averages of representation numbers of symmetric
matrices.
