A Weighted Universality Theorem for Periodic Zeta-Functions

Abstract

The periodic zeta-function ζ(s; a), s = σ + it is defined for σ > 1 by the Dirichlet series with periodic coefficients and is meromorphically continued to the whole complex plane. It is known that the function ζ(s; a), for some sequences a of coefficients, is universal in the sense that its shifts ζ(s + iτ ; a), τ ∈ ℝ, approximate a wide class of analytic functions. In the paper, a weighted universality theorem for the function ζ(s; a) is obtained.

Keywords:

• Hurwitz zeta-function
• Mergelyan theorem
• periodic zeta-function
• universality

AMS Subject Classification:

• 11M41