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Mean Value Properties of the Hurwitz Zeta-Function.
MATHEMATICA SCANDINAVICA, 1992 Let \(\zeta^* (s,x) = \zeta (s,x + 1)\), where \(\zeta (s,a)\) \((0 < a \leq 1)\) is the Hurwitz zeta-function. The author proves that \[ \int^ 1_ 0 \left | \zeta^* \Bigl( {1 \over 2} + it, x \Bigr) \right |^ 2 dx = \log \left( {t \over 2 \pi} \right) + \gamma - 2 \text{Re} {\zeta (1/2 + it) \over 1/2 + it} + O \left( {1 \over t} \right), \] where ...
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Real zeros of Hurwitz–Lerch zeta and Hurwitz–Lerch type of Euler–Zagier double zeta functions [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2015 AbstractLet 0 < a ⩽ 1, s, z ∈ ${\mathbb{C}}$ and 0 < |z| ⩽ 1. Then the Hurwitz–Lerch zeta function is defined by Φ(s, a, z) ≔ ∑∞n = 0zn(n + a)− s when σ ≔ ℜ(s) > 1. In this paper, we show that the Hurwitz zeta function ζ(σ, a) ≔ Φ(σ, a, 1) does not vanish for all 0 < σ < 1 if and only if a ⩾ 1/2.
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Integral means for k-uniformly starlike Hurwitz-Lerch Zeta fractional power functions [PDF]
, 2014 Uzoamaka A. Ezeafulukwe, Maslina Darus
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Certain Identities of a General Class of Hurwitz-Lerch Zeta Function of Two Variables
, 2022 M. A. Pathan +2 more
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MAJORIZATION FOR CERTAIN CLASSES OF ANALYTIC FUNCTIONS USING HURWITZ LERCH ZETA FUNCTION [PDF]
, 2013 K. Thilagavathi, G. Murugusundaramoorthy
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A Probabilistic Interpretation of the Hurwitz Zeta Function
Advances in Mathematics, 1993 Es sei \(\chi_ A\) die charakteristische Funktion einer Menge \(A\subset\mathbb{R}\). \textit{S. W. Golomb} [J. Number Theory 2, 189-192 (1970; Zbl 0198.381)] definierte bei beliebigem \(s>1\) auf \(\mathbb{N}\) das Wahrscheinlichkeitsmaß \[ Q_ s(A)={1\over {\zeta(s)}} \sum_{n=1}^ \infty \chi_ A(n)n^{-s} \qquad (A\subset\mathbb{N}).
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A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks. [PDF]
Entropy (Basel), 2021 Jung H, Phoa FKH.
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Heavy Tails and the Shape of Modified Numerals. [PDF]
Cogn Sci, 2022 Carcassi F, Szymanik J.
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Testing the Bethe ansatz with large N renormalons. [PDF]
Eur Phys J Spec Top, 2021 Mariño M, Miravitllas R, Reis T.
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