The Igusa Zeta Function Associated with a Composite Power Function on the Space of Rectangular Matrices

On the space of real rectangular $(n\times m)$ matrices, we introduce a composite power function and study the zeta integral associated with it. We describe the properties of the Igusa zeta function on the basis of the properties of a generalized composite power function and establish a functional relation for the zeta integral. As a result, the Fourier transform of a generalized composite power function is found in explicit form.