Related papers: On some properties of Riemann zeta function on cri…

We prove some new bounds for the maximum of Riemann zeta-function on very short segments of the critical line. All the theorems are based on the Riemann hypothesis.

This paper continues a series of investigations on converging representations for the Riemann Zeta function. We generalize some identities which involve Riemann's zeta function, and moreover we give new series and integrals for the zeta…

In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis.

The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta…

This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.

This is a review of some of the interesting properties of the Riemann Zeta Function.

We present highlights of computations of the Riemann zeta function around large values and high zeros. The main new ingredient in these computations is an implementation of the second author's fast algorithm for numerically evaluating…

In this paper we give criteria about estimation of derivatives of the Riemann Zeta Function on the line $\sigma=1$.

The purpose of this paper is to prove that the so-called Quasi-Riemann Hypothesis for the Zeta-function implies the Riemann Hypothesis

This paper considers some infinite series involving the Riemann zeta function.

We present drawings on the complex plane of the lines Im(zeta(s))=0 and Re(zeta(s))=0. This allow to illustrate many properties of the zeta function of Riemann. This is an expository paper. It does not pretend to prove any new result about…

Assuming the Riemann Hypothesis we obtain an upper bound for the moments of the Riemann zeta-function on the critical line. Our bound is nearly as sharp as the conjectured asymptotic formulae for these moments. The method extends to moments…

In this paper, we give a connection between the Riemann hypothesis and uniqueness of the Riemann zeta function and an analogue for L-functions.

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 describe some experiments that show a connection between elliptic curves of high rank and the Riemann zeta function on the one line. We also discuss a couple of statistics involving $L$-functions where the zeta function on the one line…

Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta…

We present a quantum mechanical model which establishes the veracity of the Riemann hypothesis that the non-trivial zeros of the Riemann zeta-function lie on the critical line of $\zeta(s)$.

In the present paper the asymptotic formulae for the first moment of the Riemann zeta-function on the critical line is proven under assumption of the Riemann Hypothesis.

In this paper we set up the theory of acid zeta function and ajoint acid zeta function, based on the theory, we point out a reason to doubt the truth of the Riemann hypothesis and also as a consequence, we give out some new RH equivalences.

We have proposed a regularization technique and apply it to the Euler product of zeta functions in the part one. In this paper that is the second part of the trilogy, we give another evidence to demonstrate the Riemann hypotheses by using…