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ON THE UNIVERSALITY OF THE HURWITZ ZETA-FUNCTION
International Journal of Number Theory, 2012It is known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that its shifts ζ(s + iτ, α), τ ∈ ℝ, approximate with a given accuracy any analytic function uniformly on compact subsets of the strip D = {s ∈ ℂ : ½ < σ < 1}. Let H(D) denote the space of analytic functions on D equipped with
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Sums Involving the Hurwitz Zeta Function
The Ramanujan Journal, 2001Let as usual \(\zeta(s,\alpha)\) be the Hurwitz zeta-function and \(\Gamma(s)\) be the Euler gamma function. Let \(\Re\alpha>0\), \(\Re p>0\), \(\Re q>0\) and \(|z|
Kanemitsu, Shigeru +2 more
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On a problem analogues to Lehmer’s and Hurwitz zeta-function
Applied Mathematics and Computation, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Qing Tian, Shujuan Cao, Chunxiao Yang
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Hurwitz Type Multiple Genocchi Zeta Function
AIP Conference Proceedings, 2009Main purpose of this paper is to construct higher‐order w‐q‐Genocchi numbers and polynomials by using p‐adic q‐deformed fermionic integral on Zp. We derive some interesting identities related to higher‐order w‐q‐Genocchi numbers and polynomials. We also construct Hurwitz type multiple w‐Genocchi zeta function which interpolates these polynomials at ...
Hacer Ozden +4 more
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On Joint Universality of the Riemann and Hurwitz Zeta-Functions
Mathematical Notes, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Hurwitz Zeta Function and the Lerch Zeta Function
2017In this chapter we will discuss formulas we have developed for the evaluation of certain zeta functions. We will need them later for the numerical computation of the spectrum of the transfer operator. The implementations of these zeta functions are in a sense the heart of our computations, so we need to be very careful.
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New Aspects of Universality of Hurwitz Zeta-Functions
Analysis Mathematica, 2023Let \(D =\{ s \in \mathbb{C} : 1/2 < \sigma < 1\}.\) Denote by \(\mathcal{K}\) the class of compact subsets of the strip \(D\) with connected complements, and by \(H(K)\) with \(K \in \mathcal{K}\) the class of continuous functions on \(K\) that are analytic in the interior of \(K\).
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Inequalities for the Hurwitz zeta function
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2000Let be the Hurwitz zeta function. Furthermore, let p > 1 and α ≠ 0 be real numbers and n ≥ 2 be an integer. We determine the best possible constants a(p, α, n), A(p, α, n), b(p, n) and B(p, n) such that the inequalities and hold for all positive real numbers x1,…,xn.
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On the Hurwitz Zeta Functions with Algebraic Irrational Parameter
Mathematical Notes, 2019Following notations and definitions used for the universality in Voronin's sense property, denote by \(K\) a compact subset of the strip \(D:=\{s \in \mathbb{C}: 1/2 < \sigma
Balčiūnas, Aidas +2 more
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The Riemann Zeta Function and the Hurwitz Zeta Function
2022Anthony A. Ruffa, Bourama Toni
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