On Siegel series for Hermitian forms (Q580409)

Let K be an imaginary quadratic number field of class number 1. Consider a complex number s with \(Re(s)>4\) and an over K semi-integral positive semi-definite Hermitian \(2\times 2\) matrix H. The author studies the singular series b(s,H), which appears in the Fourier expansion of the Eisenstein series (related with K) on the Hermitian half-space of degree 2. An explicit formula for b(s,H) in terms of Dirichlet series is derived. Then the author generalizes \textit{G. Kaufhold}'s result [Math. Ann. 137, 454-476 (1959; Zbl 0086.067)] and obtains meromorphic continuation and functional equation for the nonanalytic Eisenstein series.