A semi-ordinary p-stabilization of Siegel Eisenstein series for symplectic groups and its p-adic interpolation

For a given rational prime p, we define a certain p-stabilization of holomorphic Siegel Eisenstein series for the symplectic group of arbitrary genus. In addition, we derive an explicit formula for the Fourier coefficients and conclude their p-adic interpolation problems. More precisely, we construct a Lambda-adic Siegel modular form of tame level 1, in the sense of A. Wiles, H. Hida and R.L. Taylor that specializes some p-adic analytic families of the above-mentioned p-stabilized Siegel Eisenstein series with trivial Nebentypus and Siegel Eisenstein series with some non-trivial Nebentypus of p-power conductor simultaneously. This can be viewed as a natural generalization of the ordinary Lambda-adic Eisenstein series of genus 1.