Joint approximation by zeta-functions of cusp forms

摘要

In the paper, we consider a collection of zeta-functions associated with normalized Hecke eigen-cusp forms for the full modular group, and prove a theorem on the simultaneous approximation of a collection of analytic functions from a wide class by a collection of discrete shifts of the above zeta-functions. For this, a hypothesis on the linear independence of a certain set is applied.