相关论文: Gram's Law and the Argument of the Riemann Zeta Fu…

Some Titchmarsh results following Gram's law are improved in this paper.

Some statements concerning the distribution of imaginary parts of zeros of the Riemann zeta\,-function are established. These assertions are connected with so\,-called `Gram's law' or `Gram's rule'. In particular, we give a proof of several…

A simple and elementary derivation of values at integer points for the Riemann's zeta and related functions is reported.

This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation…

This paper has been withdrawn by the author due to an error in section 7. There is a new version: arXiv:1011.3352.

An analog of the Riemann hypothesis is proved in this paper. Some new integral equations for the functions $\pi(x)$ and $R(x)$ follows. A new effect that is shown is that these function - with essentially different behavior - are the…

This paper extends the work done by Titchmarsh on Gram's Law (an attempt to locate the zeroes of the zeta-function on the critical line). Herewith it is shown that a positive proportion of Gram intervals violate Gram's Law; and also that a…

We have looked at the evaluation of the Riemann Zeta function at odd arguments and have provided a simple formula to approximate the value with exponential convergence. We have compared it with various other formulae present in literature.…

The paper was withdrawn by the author. It contained various errors.

This is an elementary note. It corrects a mistake in the reformulation of the Riemann Hypothesis in J. Havil's book Gamma: Exploring Euler's Constant.

Glasser's Master Theorem arXiv:1308.6361v2 is essentially a restatement of Cauchy's integral Theorem reduced to a specialized form. Here we extend that theorem by introducing two new parameters, but still retain a simple form. Because of…

We present an elementary, short and simple proof of the validity of the Lindel\"of hypothesis about the Riemann zeta-function. The obtained estimate and classical results by Bohr-Landau and Littlewood disprove Riemann's hypothesis.

An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.

We rewrite Riemann Zeta function as a sum over the primes. Each term of the sum is a product that depends only on the summation index (a prime) and the primes following it.

A proof of the Riemann hypothesis using the reflection principle is presented.

The paper presents several new sufficient conditions, as well as new equivalent criteria for the classical Riemann Hypothesis. Noteworthy are also other statements and remarks about $\zeta$ to be found throughout the paper.

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

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

A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.

This paper has been withdrawn by the author for further investigation.