Related papers: Acid zeta function and ajoint acid zeta function
In this paper, we introduce the method of adding additional factors and a parameter to multiple zeta values and prove some generalizations of the duality theorem and several relations among multiple zeta values. In particular, we are able…
Global mapping properties of the Riemann Zeta function are used to investigate its non trivial zeros.
The goal of this paper is to give a relatively simple proof of some known zero density estimates for Riemann zeta function which are sufficiently strong to break the density hypothesis in a nontrivial part of the critical strip. Apart from…
We make plausible the existence of counterexamples to the Riemann hypothesis located in the neighbourhood of unusually large peaks of $\vert \zeta \vert$. The main ingredient in our argument is an identity which links the zeros of a…
This article describes a sequence of rational functions which converges locally uniformly to the zeta function. The numerators (and denominators) of these rational functions can be expressed as characteristic polynomials of matrices that…
We solve problem 11585 proposed by B. Burdick, AMM June-July 2011 {\bf 118} (6), p. 558 for the sum of certain products of Riemann zeta function values. We further point out an alternating sum analog, and then present and prove different…
In our previous papers, we have introduced within the theory of the Riemann zeta function the following notions: Jacob's ladders, oscillating systems, $\zeta$-factorization, metamorphoses, \dots In this paper we obtain $\zeta$-analogue of…
The main objective of this paper is to introduce a new extension of Hurwitz-Lerch Zeta function in terms of extended beta function. We then investigate its important properties such as integral representations, differential formulas, Mellin…
L. de Branges proposed an approach to the Riemann hypothesis using certain positivity conditions. In this paper, the authors examine this approach and indicate its difficulty.
We prove Riemann hypothesis. Method is to show the convexity of function which has zeros on open critical strip the same as zeta function.
Commenting on an observation of Prof. Edwards, this note presents a method of evaluation of $\zeta(2n)$ that follows easily from Riemann's own representation of the zeta function.
We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the…
We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a…
In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of…
We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…
In this paper, a positive answer to the Riemann hypothesis is given by using a new result that predict the exact location of zeros of the alternating zeta function on the critical strip.
This paper presents a new approach towards the Riemann Hypothesis. On iterative expansion of integration term in functional equation of the Riemann zeta function we get sum of two series functions. At the `non-trivial' zeros of zeta…
In this paper, some new results are reported for the study of Riemann zeta function $\zeta(s)$ in the critical strip $0<Re(s)<1$, such as $\zeta(s)$ expressed in a generalized Euler product only involving prime numbers. Particularly, some…
This paper studies combinations of the Riemann zeta function, based on one defined by P.R. Taylor, which was shown by him to have all its zeros on the critical line. With a rescaled complex argument, this is denoted here by ${\cal T}_-(s)$,…
Starting from the Euler's identity, the author improved Riemann's results, discovered the relationship between the Riemann Zeta function and the prime function, and obtained two new corollaries based on Riemann hypothesis is tenable. From…