Results 1 to 10 of about 6,967 (160)
Mathematics, 2018 Riemann’s method is one of the definitive ways of solving Cauchy’s problem for a second order linear hyperbolic partial differential equation in two variables. The first review of Riemann’s method was published by E.T.
Peter J. Zeitsch
doaj +4 more sources
International Journal of Mathematics and Mathematical Sciences, 2004 We consider the modified q-analogue of Riemann zeta function which is defined by ζq(s)=∑n=1∞(qn(s−1)/[n]s ...
Taekyun Kim
doaj +2 more sources
Some identities related to Riemann zeta-function
Journal of Inequalities and Applications, 2016 It is well known that the Riemann zeta-function ζ ( s ) $\zeta(s)$ plays a very important role in the study of analytic number theory. In this paper, we use the elementary method and some new inequalities to study the computational problem of one kind of
Lin Xin
doaj +3 more sources
A note on the Riemann ξ-function
Lietuvos Matematikos Rinkinys, 2000 We prove that for σ > 4.5, inf {ℜ(ξ'(σ + it)/ξ(σ + it) ) : - ∞ < t < ∞} = ξ'(σ)/ξ(σ). This improves the result obtained by Lagarias.
Ramūnas Garunkštis
doaj +5 more sources
The Riemann method for equations with a dominant partial derivative (A Review) [PDF]
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2021 This review article is devoted to a class of linear equations with a dominant (leading) partial derivative of the form \((D+M)u=f\), where \(Du\) is a mixed partial derivative, and \(M\) is a linear differential operator containing the derivatives of the
Aleksey N. Mironov +2 more
doaj +1 more source
The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation
Journal of Nigerian Society of Physical Sciences, 2022 The analysis of the derivation of the Riemann Analytic Continuation Formula from Euler’s Quadratic Equation is presented in this paper. The connections between the roots of Euler’s quadratic equation and the Analytic Continuation Formula of the Riemann ...
Opeyemi O. Enoch +2 more
doaj +1 more source
ON THE FUNCTIONAL INDEPENDENCE OF THE RIEMANN ZETA-FUNCTION
Mathematical Modelling and Analysis, 2023 In 1973, Voronin proved the functional independence of the Riemann zeta-function ζ(s), i.e., that ζ(s) and its derivatives do not satisfy a certain equation with continuous functions. In the paper, we obtain a joint version of the Voronin theorem.
Garbaliauskienė, Virginija +2 more
openaire +3 more sources
On Riemann's Functional Equation
The Annals of Mathematics, 1957 constant factor) if it satisfies Riemann's functional equation. This result was placed in an altogether more general setting by Hecke's work [9] on the correspondence between Dirichlet series with given signature (introduced by him), and modular functions. This paper is also concerned with that problem, but from a different approach.
Chandrasekharan, K., Mandelbrojt, Szolem
openaire +4 more sources
Riemann’s zeta function and beyond [PDF]
Bulletin of the American Mathematical Society, 2003 In recent years L L -functions and their analytic properties have assumed a central role in number theory and automorphic ...
Gelbart, Stephen S., Miller, Stephen D.
openaire +3 more sources
Four Variants of Riemann Zeta Function
Mathematics, 2022 By means of the generating function method and Dougall’s formulae for bilateral hypergeometric series, we examine four classes of infinite series, which may be considered as variants of Riemann zeta function. Several summation formulae are established in
Nadia N. Li, Wenchang Chu
doaj +1 more source