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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)

On 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 joint universality for periodic Hurwitz zeta-functions

Analysis (Germany), 2006
We prove a joint universality theorem for the Hurwitz zeta-functions with periodic coefficients.
Antanas Laurincikas
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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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On joint universality of periodic Hurwitz zeta-functions

Lithuanian Mathematical Journal, 2008
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A Laurincikas, Laurincikas A
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A joint universality theorem for periodic Hurwitz zeta-functions. II

Lithuanian Mathematical Journal, 2009
The aim of this paper is to prove a joint universality theorem for the functions \(\zeta(s, \alpha_1; \mathfrak A_1), \ldots,\) \(\zeta(s, \alpha_r; \mathfrak A_r)\) without using the hypothesis on the rank of the matrix \(A\) [\textit{A. Javtokas} and the first author [Bull. Aust. Math. Soc. 78, No. 1, 13--33 (2008; Zbl 1228.11136)]. Let \[ L(\alpha_1,
A Laurincikas, Laurincikas A
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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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