ANALYTIC PROPERTIES OF STANDARD ZETA-FUNCTIONS OF SIEGEL MODULAR-FORMS

It is proved that standard zeta functions (analogs of the zeta functions of Rankin and Shimura) for holomorphic cusp forms with respect to congruence subgroups of the form of the Siegel modular group of arbitrary even degree have a meromorphic continuation. For the case, with some additional restrictions, it is proved that the zeta functions are holomorphic except for a finite number of poles, and a functional equation is obtained. Bibliography: 9 titles. © 1979 IOP Publishing Ltd.