The Approximation of Analytic Functions Using Shifts of the Lerch Zeta-Function in Short Intervals

In this paper, we obtain approximation theorems of classes of analytic functions by shifts L(λ,α,s+iτ) of the Lerch zeta-function for τ∈[T,T+H] where H∈[T27/82,T1/2]. The cases of all parameters, λ,α∈(0,1], are considered. If the set {log(m+α):m∈N0} is linearly independent over Q, then every analytic function in the strip {s=σ+it∈C:σ∈(1/2,1)} is approximated by the above shifts.