ON HERMITIAN EISENSTEIN SERIES OF DEGREE 2

We consider the Hermitian Eisenstein series E(K) k of degree 2 and weight k associated with an imaginary-quadratic number field K and determine the influence of K on the arithmetic and the growth of its Fourier coefficients. We find that they satisfy the identity E(K)2 4 = E(K) which is well-known for Siegel modular forms of degree 2, if and only if K = Q(root-3). As an appli-8, cation, we show that the Eisenstein series E(K) k , k = 4, 6, 8,10,12 are algebraically independent whenever K =6 Q(root-3). The difference between the Siegel and the restriction of the Hermitian to the Siegel half-space is a cusp form in the Maass space that does not vanish identically for sufficiently large weight; however, when the weight is fixed, we will see that it tends to 0 as the discriminant tends to -infinity. Finally, we show that these forms generate the space of cusp forms in the Maass Spezialschar as a module over the Hecke algebra as K varies over imaginary-quadratic number fields.