Riemann zeta function
The Riemann zeta function
... CHAPTER TWO: HISTORICAL BACKGROUND OF THE ZETA FUNCTION Introduction ..s. Properties of the Riemann Zeta Function ....[r] ...
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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 ...
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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 zeta function by ...
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Common Properties of Riemann Zeta Function, Bessel Functions and Gauss Function Concerning Their Zeros
... the Riemann zeta function on the y -axis and separate themselves from the main bulk of zeros in a considered order which do not lie on the imaginary ...
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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 ...
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Fast convergence of generalized DeTemple sequences and the relation to the Riemann zeta function
... We remark that the expressions from Theorem . and Corollary . concern the ex- pansion of Euler’s constant in terms of the Riemann zeta function evaluated at positive odd integers. Therefore the ...
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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 ...
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On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip
... Xiaoxue [7] came up with a computational formula for the case s = 4, and Xu [8] proved two computational formulas that are related to the Riemann zeta function at s = 4, 5, using a slightly different ...
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Some computational formulas related the Riemann zeta function tails
... Abstract In this paper we present two computational formulae for one kind of reciprocal sums related to the Riemann zeta-function at integer points s = 4, 5, which answers an open proble[r] ...
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A Necessary Condition for the Existence of the Nontrivial Zeros of the Riemann Zeta Function
... gamma function valid on the entire complex ...sine function, the functional equation implies that ζ(s) has simple zeroes at negative even integers, which are known as the trivial zeros of ...extended ...
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The Inconsistency Problem of Riemann Zeta Function Equation
... the Riemann Zeta function equation is inconsistent on the real axis of complex ...of Riemann Zeta function equation, it is the point of ...
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A Note on Riemann Zeta Function
... The Riemann Zeta Function is an essential special function in analytical number theory; its connection to the distribution of prime numbers was the motivation to expand its domain from real ...
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q Riemann zeta function
... of Riemann zeta function at negative integers in the same way that Riemann zeta function interpolates Bernoulli numbers at negative ...
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On a mollifier of the perturbed Riemann zeta function
... It should also be remarked that Bui [2] suggests that the bound obtained in this paper can be attained using the twisted second moment of the Riemann zeta-function due to Balasubramanien et. al. [1] ...
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A more accurate half-discrete Hardy-Hilbert-type inequality with the best possible constant factor related to the extended Riemann-Zeta function
... cosecant function with a best possible constant factor expressed by the extended Riemann- zeta function is proved, which is an extension of ...
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On Maslanka's Representation for the Riemann Zeta Function
... A rigorous proof is given of the hypergeometric-like representation of the Riemann zeta function ζs discovered by Maslanka as a series of Pochhamer polynomials with coefficients depending [r] ...
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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] derived deeper results ...
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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 the special values s ...
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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 real ...
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Some Ramanujan Integrals Associated with Generalized Riemann Zeta Function and Multivariable Gimel-Function
... The importance of our all the results lies in their manifold generality. Firstly, in view of general arguments utilized in these single infinite integrals, we can obtain a large simpler single infinite integrals, ...
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