| Abstract [eng] |
In this paper, we prove the theorems on the simultaneous approximation of a pair of analytic functions by discrete shifts (π(π +ππβ1),π(π +ππβ2,πΌ)), β1>0, β2>0 of the Riemann zeta function π(π ) and Hurwitz zeta function π(π ,πΌ). The lower density and density of the above approximating shifts are considered in short intervals [π,π+π] as πββ with π=π(π). If the set {(β1logπ:πββ),(β2log(π+πΌ):πββ0),2π} is linearly independent over β, the class of approximated pairs is explicitly given. If πΌ and β1, β2 are arbitrary, then it is known that the set of approximated pairs is a certain non-empty closed subset of β2(Ξ), where β(Ξ) is the space of analytic functions on the strip Ξ={π ββ:1/2<Reπ <1}. For the proof, limit theorems on weakly convergent probability measures in the space π»2(Ξ) are applied. |
