Koecher-Maass series for positive definite Fourier coefficients of real analytic Siegel-Eisenstein series of degree 2

Abstract

It is shown that the Koecher-Maass series for positive definite Fourier coefficients of a real analytic Siegel-Eisenstein series of degree 2 has a meromorphic continuation and a simple functional equation.

Rankin–selberg Convolutions of Noncuspidal Half-Integral Weight Maass Forms in the Plus Space

“…The positive definite case was first proved in [24]. The only special case for degree 2 indefinite Fourier coefficients was treated in [25], which can be proved again from Theorem 4.…”