[PDF] Top 20 On some historical aspects of the theory of Riemann zeta function
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On some historical aspects of the theory of Riemann zeta function
... detail some armations of ...entire function factorization, we report textual words of Picard (see (Picard 1897) and (Dugac 1973, Section ...the theory of entire functions, as we will see later ... See full document
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From Veneziano to Riemann: A string theory statement of the Riemann hypothesis
... string theory, through the form of the Veneziano amplitude, should know about the Riemann zeta function [12], and thence about the Riemann ...string theory, itself a subject of ... See full document
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Calculation of the Riemann Zeta-function on a Relativistic Computer
... the Riemann ζ-function represented by a divergent series in the plane of the complex argument is performed using the methods of the general theory of ...of some material particle in a curved ... See full document
7
Certain relationships among polygamma functions, Riemann zeta function and generalized zeta function
... The Riemann zeta function ζ (s) in (.) plays a central role in the applications of complex analysis to number theory. The number-theoretic properties of ζ (s) are exhibited by the following ... See full document
11
On the Prime Geodesic Theorem for Non Compact Riemann Surfaces
... number theory relating the zeroes of the Riemann zeta function to prime numbers, Selberg [1] introduced a zeta function whose analytic properties are encoded in the Selberg trace ... See full document
13
Vol 9, No 1 (2018)
... the theory of Riemann zeta ...the Riemann zeta ...“The theory of the Riemann zeta-function” published in 1951 [10, 11, ...a theory of ... See full document
5
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 ... See full document
10
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
5
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 ...matter theory quasi-particles that are neither ... See full document
13
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 ... See full document
15
The Inconsistency Problem of Riemann Zeta Function Equation
... The Riemann hypothesis is so famous, also due to the fact that it has become the important basis of modern prime number distribution ...distribution theory was extended from the real domain to the complex ... See full document
10
Some identities related to Riemann zeta function
... the Riemann zeta-function ζ (s) plays a very important role in the study of analytic number ...and some new inequalities to study the computational problem of one kind of reciprocal sums ... See full document
6
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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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
7
A q analog of Euler's decomposition formula for the double zeta function
... [6] D. Bowman and D. M. Bradley, Multiple polylogarithms: a brief survey, q-Series with Applica- tions to Combinatorics, Number Theory, and Physics (Urbana, Ill, 2000) (B. C. Berndt and K. Ono, eds.), Contemp. ... See full document
6
Integral and Computational representations of Generalized Hurwitz Lerch Zeta Function φ(a 1 z,s,a)
... Generalized Hurwitz – Lerch Zeta function Φ( , , )are established.Certain known integral representation for generalized Riemann Zeta function is obtained as special cases of main ... See full document
6
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
... These results hold for any value of a and for any value of L. This means that even though the expression for 𝛽 does not at first sight appear to converge, we could argue that the derivative will not change sign when L ... See full document
8
An integral involving the generalized zeta function
... of the Riemann zeta function at the point -1, a quantity that arises in the evaluation of determinants of Laplacians on compact Riemann surfaces... WORDS AND PHRASES..[r] ... See full document
8
A Double Inequality for the Ratio of Two Consecutive Bernoulli Numbers
... [12] J. Higgins, Double series for the Bernoulli and Euler numbers, J. London Math. Soc. 2nd Ser. 2 (1970), 722–726; Available online at http://dx.doi.org/10.1112/jlms/2.Part_4.722. [13] S. Jeong, M.-S. Kim, and J.-W. ... See full document
7
On Some Aspects of Educational Network
... Social networking often involves grouping specific individuals or organizations together. Most of the social networking websites focus on one or other interests, but some sites have no affiliations towards any of ... See full document
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