Gram points in the theory of zeta-functions of certain cusp forms

Abstract In the paper, an analogue of the Gram points used in the theory of the Riemann zeta-function is introduced for zeta-functions of normalized Hecke-eigen cusp forms of weight κ. Some analytic properties of those points are studied, and the first ten Gram points for κ ⩽ 12 are calculated. The main attention is devoted to the universality of zeta-functions of cusp forms on the approximation of analytic functions by shifts involving the sequence of Gram points.