A Weighted Universality Theorem for Periodic Zeta-Functions. Issue 1 (2nd January 2017)

• Record Type: Journal Article
• Authors: Macaitienė, Renata; Stoncelis, Mindaugas; Šiaučiūnas, Darius
• Is Part Of: Mathematical modelling and analysis. Volume 22:Issue 1(2017)
• Page Start: 95
• Page End: 105
• Publication Date: 2017-01-02
• Subjects: Hurwitz zeta-function -- Mergelyan theorem -- periodic zeta-function -- universality; 11M41; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2017.1269373
• Languages: English
• ISSNs: 1392-6292

Abstract

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.