A Weighted Universality Theorem for Periodic Zeta-Functions. Issue 1 (2nd January 2017) - Macaitienė, Renata; Stoncelis, Mindaugas; Šiaučiūnas, Darius
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.