by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...

The computation of the complex zeros of an incomplete Riemann zeta function defined in an earlier paper is extended and new zero trajectories are given. A second incomplete Riemann zeta function is denned and its zero trajectories are investigated numerically as functions of the upper limit X of the definition integral. It becomes apparent that there exist three different classes of zero trajec...

Let F be an algebraic number field. Recently, L. Weng introduced zeta functions of rank n associated to F as a generalization of the Iwasawa-Tate zeta integral from the Arakelov geometric point of view. In the article, we call them the Weng zeta function of rank n. In the case of rank one, the Weng zeta function coincide with the Dedekind zeta function of F . The background and precise definiti...

Abstract The Riemann zeta distribution, defined as the one whose characteristic function is the normalised Riemann zeta function, is an interesting example of an infinitely divisible distribution. The infinite divisibility of the distribution has been proved with recourse to the Euler product of the Riemann zeta function. In this paper, we look at multiple zeta-star function, which is a multi-d...

The Riemann zeta function ζ(s) is defined by ζ(s) = ∑∞ n=1 1 ns for R(s) > 1 and may be extended to a regular function on the whole complex plane excluding its unique pole at s = 1. The Riemann hypothesis is a conjecture made by Riemann in 1859 asserting that all non-trivial zeros for ζ(s) lie on the line R(s) = 12 , which has a broad application in every branch of mathematics. The density hypo...

The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler’s results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. Here, we establish a q-analog of Euler’s decomposition formula. More specifically, we s...

Mathematisch-naturwissenschaftlichen Fakultät Doctor of Philosophy Twisted Second Moments and Explicit Formulae of the Riemann Zeta-Function by Nicolas Martinez Robles Verschiedene Aspekte, die analytische Zahlentheorie und die Riemann zeta-Funktion verbinden, werden erweitert. Dies beinhaltet: 1. explizite Formeln, die eine Verbindung zwischen der Möbiusfunktion und den nichttrivialen Nullstel...