Fourier -Jacobi coefficients of Eisenstein series on unitary group

This thesis is dedicated to the calculation of Fourier-Jacobi coefficients of an Eisenstein series on a degree four nonsplit unitary group when the Eisenstein series is defined through the pull back of an Siegel Eisenstein seires on a quasi-split unitary group. Also the inner product of the Fourier-Jacobi coefficients with theta functions is worked out. After analyzing the arithmetic properties of these coefficents, the arithmetic properties of Eisenstein series can be obtained.