[PDF] Top 20 The Riemann zeta function
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The Riemann zeta function
... CHAPTER TWO: HISTORICAL BACKGROUND OF THE ZETA FUNCTION Introduction ..s. Properties of the Riemann Zeta Function ....[r] ... See full document
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Some identities related to Riemann zeta function
... the Riemann zeta-function basically can be summarized in three aspects: (A) the estimation of the order for the Riemann zeta- function; (B) the mean value theorem for the ... 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 real ... See full document
8
Applications of Wirtinger Inequalities on the Distribution of Zeros of the Riemann Zeta Function
... the Riemann zeta-function on the critical ...the zeta-function on the critical line, and because of its applicability in studying the distribution of prime numbers and divisor ...from ... See full document
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On some historical aspects of the theory of Riemann zeta function
... that Riemann began already to study elliptic and Abelian functions since the late 1840s, because this subject, in the meantime, has become of a certain vogue in ...Riemannian function theory work, he wishes ... See full document
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Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
... functions, Riemann zeta function, and generalized zeta function by mainly modifying Chen’s method ...lambda function λ(s) defined ... See full document
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A new generalization of the Riemann zeta function and its difference equation
... generalized Riemann zeta function has simple connections with the recently defined eBE and eFD functions, which have also found another use in ...anyon function as they interpolate very ... See full document
13
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 ... See full document
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Common Properties of Riemann Zeta Function, Bessel Functions and Gauss Function Concerning Their Zeros
... the Riemann hypothesis but during the work we found a further, as it seems, essential building stone for its proof by the second mean-value approach which is represented in ...a function with a possible ... See full document
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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] ... See full document
7
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 ... See full document
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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 ... See full document
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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] ... See full document
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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] ... 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] derived deeper results ... See full document
13
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 ... See full document
10
q Riemann zeta function
... of Riemann zeta function was studied by Cherednik (see ...of Riemann zeta function at negative ...of zeta function interpolates q -Bernoulli numbers at negative ... See full document
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Some Ramanujan Integrals Associated with Generalized Riemann Zeta Function and Multivariable Gimel-Function
... integration ans summations which is justified under the conditions mentioned above, Now interchanging the order of integrations which is justified under the conditions mentioned above, evaluating the inner -integral with ... See full document
8
Calculation of the Riemann Zeta-function on a Relativistic Computer
... the Riemann ζ-function of a complex argument is considered in the paper, using the effects of the general theory of ...the Riemann ζ-function. The formulation of the Riemann hypothesis ... See full document
7
Summability methods based on the Riemann Zeta function
... In this section we compare the strength of the zeta method and the zeta matrix methods to several well-known summability methods.. Throughout this section C a denotes the Cesaro summabil[r] ... See full document
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