Laurinčikas, A. P. Universality of composite functions of periodic zeta functions. (English. Russian original) Zbl 1295.11096 Sb. Math. 203, No. 11, 1631-1646 (2012); translation from Mat. Sb. 203, No. 11, 105-120 (2012). Summary: In the paper, we prove the universality, in the sense of Voronin, for some classes of composite functions \( F(\zeta(s;\mathfrak{a}))\), where the function \( \zeta(s;\mathfrak{a})\) is defined by a Dirichlet series with periodic multiplicative coefficients. We also study the universality of functions of the form \( F(\zeta(s;\mathfrak{a}_1),\dots,\zeta(s;\mathfrak{a}_r))\). For example, it follows from general theorems that every linear combination of derivatives of the function \( \zeta(s;\mathfrak{a})\) and every linear combination of the functions \( \zeta(s;\mathfrak{a}_1),\dots,\zeta(s;\mathfrak{a}_r)\) are universal. Cited in 3 Documents MSC: 11M41 Other Dirichlet series and zeta functions 30K10 Universal Dirichlet series in one complex variable Keywords:support of a measure; periodic zeta function; limit theorem; the space of analytic functions; universality PDFBibTeX XMLCite \textit{A. P. Laurinčikas}, Sb. Math. 203, No. 11, 1631--1646 (2012; Zbl 1295.11096); translation from Mat. Sb. 203, No. 11, 105--120 (2012) Full Text: DOI