On the functional equation of the Siegel series

It is well-known that the Fourier coefficients of Siegel–Eisenstein series can be expressed in terms of the Siegel series. The functional equation of the Siegel series of a quadratic form over QpQp was first proved by Katsurada. In this paper, we prove the functional equation of the Siegel series over a non-archimedean local field of characteristic 0 by using the representation theoretic argument by Kudla and Sweet.