On Fourier Coefficients of Eisenstein Series

In this paper we wish to prove that under certain conditions the Fourier coefficients of the Eisenstein series for an arithmetic group acting on a tube domain are all rational numbers. Let G be a connected, simply-connected, semisimple, and almost Q-simple linear algebraic group defined over the rational number field Q. Let R be the real number field. Then GR is connected, and we assume that if K is a maximal compact subgroup of it, then 3£ = K\GR is a noncompact hermitian symmetric space. We also assume that the Q-rank of G is positive and that the Q-root system ô £ of G is of type C. Then the relative J?-root system RE of G is of type C and therefore X is isomorphic to a tube domain