Results 21 to 30 of about 32,458 (230)

The inverse of tails of Riemann zeta function, Hurwitz zeta function and Dirichlet L-function

AIMS Mathematics
In this paper, we derive the asymptotic formulas $ B^*_{r, s, t}(n) $ such that $ \mathop{\lim} \limits_{n \rightarrow \infty} \left\{ \left( \sum\limits^{\infty}_{k = n} \frac{1}{k^r(k+t)^s} \right)^{-1} - B^*_{r,s,t}(n) \right\} = 0, $ where $
Zhenjiang Pan, Zhengang Wu
doaj   +2 more sources

The fourth moment of the Hurwitz zeta function [PDF]

Journal für die reine und angewandte Mathematik (Crelles Journal)
Abstract We prove a sharp upper bound for the fourth moment of the Hurwitz zeta function ζ ⁢ ( s
Winston Heap, Anurag Sahay
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The Hurwitz Zeta Function as a Convergent Series [PDF]

Rocky Mountain Journal of Mathematics, 2006
New series for the Hurwitz zeta function which converge on the whole plane, except s = 1, are developed. This is applied to obtain a remarkably simple evaluation of some special values of the function.
Dwilewicz, Roman, Mináč, Ján
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New Result of Analytic Functions Related to Hurwitz Zeta Function [PDF]

The Scientific World Journal, 2013
By using a linear operator, we obtain some new results for a normalized analytic function f defined by means of the Hadamard product of Hurwitz zeta function. A class related to this function will be introduced and the properties will be discussed.
F. Ghanim, M. Darus
doaj   +2 more sources

Remark on the Hurwitz-Lerch zeta function [PDF]

Fixed Point Theory and Applications, 2013
Various generalizations of the Hurwitz-Lerch zeta function have been actively investigated by many authors. Very recently, Srivastava presented a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associated with various classes of the extended Hurwitz-Lerch zeta ...
Junesang Choi
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On an equivalent property of a reverse Hilbert-type integral inequality related to the extended Hurwitz-zeta function

Journal of Mathematical Inequalities, 2019
. We study some equivalent conditions of a reverse Hilbert-type integral inequality with a particular non-homogeneous kernel and a best possible constant factor related to the extended Hurwitz-zeta function.
M. Rassias, Bicheng Yang
semanticscholar   +2 more sources

Definite Integrals Involving Combinations of Powers and Logarithmic Functions of Complicated Arguments Expressed in Terms of the Hurwitz Zeta Function [PDF]

, 2021
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta functions.
Robert Reynolds, Allan Stauffer
semanticscholar   +3 more sources

Real zeros of the Hurwitz zeta function [PDF]

Acta Arithmetica, 2018
11 ...
Toshiki Matsusaka
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On joint universality of the Riemann zeta-function and Hurwitz zeta-functions

Journal of Number Theory, 2012
AbstractWe construct classes of composite functions of the Riemann zeta-function and Hurwitz zeta function with transcendental parameter which are universal in the sense that their shifts uniformly on compact subsets of some region approximate any analytic function. For example, the functions c1ζ(s)+c2ζ(s,α),c1,c2∈C∖{0}, eζ(s)+ζ(s,α) and sin(ζ(s)+ζ(s,α)
Antanas Laurinčikas
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On limit distribution of the Hurwitz zeta-function

Open Mathematics, 2010
Abstract The distribution of the vector (|ζ(s, α)|; ζ(s, α)), where ζ(s, α) is the Hurwitz zeta-function with transcendental parameter α, is considered and a probabilistic limit theorem is obtained. Also, the dependence between |ζ(s, α)| and ζ(s, α) in terms of m-characteristic transforms is discussed.
Laurinčikas Antanas
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