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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.

MSC:

11M41 Other Dirichlet series and zeta functions
30K10 Universal Dirichlet series in one complex variable
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