Joint discrete universality for periodic zeta-functions. II

Abstract

In the paper, for certain classes of operators F in the space of analytic functions, we prove the discrete universality for compositions F (ζ(s, α; 𝔞, 𝔟)), where ζ(s, α; 𝔞; 𝔟) is a collection consisting from periodic and periodic Hurwitz zeta-functions, i. e., the approximation of analytic functions by discrete shifts F (ζ(s + ikh, α; 𝔞; 𝔟)) with h > 0 and k = 0, 1, . . . . For this, a theorem of [12] is applied.

Mathematics Subject Classification (2010):

• Primary: 11M41
• Secondary: 41A30

Key words:

• Approximation of analytic functions
• periodic Hurwitz zeta-function
• periodic zeta-function
• universality
• Voronin theorem