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) 8, which is well-known for Siegel modular forms of degree 2, if and only if K = Q(√-3). As an application, we show that the Eisenstein series E^(K)k, k = 4, 6, 8, 10, 12 are algebraically independent whenever K 6= Q(√-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 -1. 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. [ABSTRACT FROM AUTHOR]