A remark on joint approximation by one Dirichlet series

Abstract. We consider one absolutely convergent series \(\zeta_{u_T}(s)\) connected to the Riemann zeta-function, and prove a theorem on joint approximation of analytic functions by shifts \((\zeta_{u_T}(s+it_\tau^{\alpha_1}), \dots, \zeta_{u_T}(s+i t_\tau^{\alpha_r}))\) as \(T\to\infty\), where \(\alpha_1, \dots, \alpha_r\) are fixed different positive numbers, \(t_\tau\) is the Gram function, and \(u_T\to\infty\) and \(u_T\ll T^2\) as \(T\to\infty\).