Distribution modulo 1 and universality of the Hurwitz zeta-function.

In the paper, a discrete universality theorem for the Hurwitz zeta-function ζ ( s , α ) on the approximation of analytic functions by shifts ζ ( s + i τ , α ) when τ takes values from the set { k β h : k = 0 , 1 , … } with fixed 0 < β < 1 and h > 0 is obtained. For its proof, the uniform distribution modulo 1 is applied. [ABSTRACT FROM AUTHOR]