[PDF] Top 20 On Evaluation of Riemann Zeta function ζ(s)
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On Evaluation of Riemann Zeta function ζ(s)
... As a matter of fact, many other recent investigations and important results on the subject of the Riemannian Zeta function ζ(s) can be found in the papers [15, 16, 17, 18, 20, 21] by H.M. ... See full document
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Integral and Computational representations of Generalized Hurwitz Lerch Zeta Function φ(a 1 z,s,a)
... This article presents a systematic investigation of various integral and computational representations , ). In this paper new results for are established.Certain known integral representation for generalized ... See full document
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Some identities related to Riemann zeta function
... the Riemann zeta-function ζ (s) plays a very important role in the study of analytic number ...the Riemann zeta-function at the integer point s ≥ 2, and for ... See full document
6
Calculation of the Riemann Zeta-function on a Relativistic Computer
... the Riemann ζ-function using relativistic effects, or, more precisely, effects of the general theory of relativity ...the ζ-function of a complex ...the ζ-function in the ... See full document
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Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
... the Riemann zeta function ζ (s) and the Hurwitz zeta function ζ (s,a) have been ...functions, Riemann zeta function, and generalized ... See full document
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On some historical aspects of the theory of Riemann zeta function
... partition function of an arbitrary thermodynamical system, often the Lee-Yang model runs well when is applied to the state equa- tion and its possible ...with zeta functions (and the Weil conjectures), the ... See full document
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A Necessary Condition for the Existence of the Nontrivial Zeros of the Riemann Zeta Function
... gamma function has a zero, it is obvious that both s / 2 ( s / 2 ) > 0 and ( 1 s ) / 2 (( 1 s ) / 2 ) > 0 in the critical ...- s), then, at least ... See full document
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A q analog of Euler's decomposition formula for the double zeta function
... double zeta function was first studied by Euler in response to a letter from Goldbach in ...this function is a decomposition formula, which ex- presses the product of two values of the Riemann ... See full document
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A new generalization of the Riemann zeta function and its difference equation
... the Riemann and Hurwitz zeta functions in the critical strip, which converges locally uniformly at ...the Riemann zeta function locally uniformly in the critical strip and gives a ... See full document
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Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta Function
... The Riemann zeta-function is one of the most studied transcendental functions, having in view its many applications in number theory, algebra, complex analysis, and statistics as well as in ...this ... See full document
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Some computational formulas related the Riemann zeta function tails
... 2. Ohtsuka, H, Nakamura, S: On the sum of reciprocal Fibonacci numbers. Fibonacci Q. 46/47, 153-159 (2008/2009) 3. Xu, Z, Wang, T: The infinite sum of the cubes of reciprocal Fibonacci numbers. Adv. Differ. Equ. ... See full document
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Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers
... Remark In the course of presenting a closed-form evaluation of some useful series in- volving the generalized zeta function ζ (s, a), Choi et al. [] made use of the identity (.) ... See full document
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Investigation of the Characteristics of the Zeros of the Riemann Zeta Function in the Critical Strip Using Implicit Function Properties of the Real and Imaginary Components of the Dirichlet Eta Function
... the Riemann zeta function (of s) in the critical strip by using the Dirichlet eta function, which has the same ...the function describing the value of the real component when the ... See full document
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On Maslanka's Representation for the Riemann Zeta Function
... In closing this introduction, we would like to point out an interesting paradox that could deserve some attention. Once the Maslanka representation is shown to be valid in the whole complex plane it is obvious that 1.1 ... See full document
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The Inconsistency Problem of Riemann Zeta Function Equation
... These results are absurd, so (12) can not be used at point and (13) can not hold. In Riemann’s original paper, (12) and its applicable condition had not been mentioned. Besides (12) is improper at , we seems unable to ... See full document
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On a mollifier of the perturbed Riemann zeta function
... Proof. This follows a similar procedure to Lemma 6.1 of [3] where the zero-free region of ζ is used. Let Y = o(T ) be a large parameter to be chosen later. By Cauchy’s theorem, Υ is equal to the sum of residues at ... See full document
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The inverses of tails of the Riemann zeta function
... The Riemann zeta function ζ (s) in the real variable s was introduced by Euler [2] in connec- tion with questions about the distribution of prime ...Later Riemann [6] ... See full document
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Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
... There are many famous unsolved problems associated with the properties of this con- stant; for example it is not known yet if the Euler constant is irrational. The Euler constant is an unusual constant and it seems ... See full document
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q Riemann zeta function
... /[n] s ), 0 < q < 1, s ∈ ...of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at ... See full document
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Certain integral representations of Stieltjes constants γn
... integral representations for the Riemann zeta function ζ (s). Our method used here is sim- ilar to those in some earlier works, but our results seem a little simpler. Some relevant con- ... See full document
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