ON THE PERIODIC HURWITZ ZETA-FUNCTION WITH RATIONAL PARAMETER.

The periodic Hurwitz zeta-function (s, α a), s = σ + it, is a generalization of the classical Hurwitz zeta-function, and is defined, for σ > 1, by the series (s, α a) = ... where a = {a_m} is a periodic sequence of complex numbers, and 0 < α ≤ 1 is a fixed parameter. In the paper, theorems on the approximation of analytic functions by discrete shifts (s + ikh, α a), k = 0, 1, . . ., h > 0, with rational α are obtained. [ABSTRACT FROM AUTHOR]