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A discrete universality Theorem for periodic Hurwitz zeta-functions

open access: yesЧебышевский сборник, 2016
LAURINCIKAS ANTANAS, MOCHOV DMITRIJ
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On joint universality for the zeta-functions of newforms and periodic Hurwitz zeta-functions (Functions in Number Theory and Their Probabilistic Aspects)

open access: yesOn joint universality for the zeta-functions of newforms and periodic Hurwitz zeta-functions (Functions in Number Theory and Their Probabilistic Aspects)
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Universality of the periodic Hurwitz zeta-function

Integral Transforms and Special Functions, 2006
In this article, the universality in the Voronin sense for the Hurwitz zeta-function with periodic coefficients is proved.
A. Javtokas, A. Laurinčikas
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The discrete universality of the periodic Hurwitz zeta function

Integral Transforms and Special Functions, 2009
The periodic Hurwitz zeta function , s=σ+it, 0 1, by and by analytic continuation elsewhere. Here {a m } is a periodic sequence of complex numbers. In this paper, a discrete universality theorem for the function with a transcendental parameter α is proved.
A. Laurinčikas, R. Macaitienė
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Functional independence of periodic Hurwitz zeta functions

Mathematical Notes, 2008
Given a periodic sequence \({\mathfrak a}:= \{a_m\mid m\in\mathbb Z, m\geq 0\}\) of complex numbers \(a_m\), let \[ \zeta(s,\alpha;{\mathfrak a})= \sum^\infty_{m=0} a_m(m+ \alpha)^{-s}. \] The so-called periodic Hurwitz zeta-function \(s\mapsto \zeta(s,\alpha;{\mathfrak a})\) can be analytically continued to the whole complex plane.
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The joint universality for periodic Hurwitz zeta-functions

Analysis, 2006
We prove a joint universality theorem for the Hurwitz zeta-functions with periodic coefficients.
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