Related papers: On infinitely divisible distributions related to t…

We show that it is possible to approximate the zeta-function of a curve over a finite field by meromorphic functions which satisfy the same functional equation and moreover satisfy (respectively do not satisfy) the analogue of the Riemann…

We give a new equivalent condition for the Riemann hypothesis consisting in an order condition for certain finite rational combinations of the values of the Riemann zeta-function at even positive integers.

We prove some uniqueness results for the Riemann zeta-function and the Euler gamma-function by virtue of shared values using the value distribution theory.

An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.

We show that there is a contradiction between the Riemann's Hypothesis and some form of the theorem on the universality of the zeta function.

Assuming the Riemann hypothesis we establish explicit bounds for the modulus of the log-derivative of Riemann's zeta-function in the critical strip.

We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations of the latter. The special…

We obtain closed form of some infinite series involving derivatives of an analogue of the Riemann xi function for Dedekind zeta function and nontrivial zeros of Dedekind zeta function assuming the Extended Riemann Hypothesis. Conversely, we…

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…

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…

We prove an equivalent of the Riemann hypothesis in terms of the functional equation (in its asymmetrical form) and the $a$-points of the zeta-function, i.e., the roots of the equation $\zeta(s)=a$, where $a$ is an arbitrary fixed complex…

Observing a multiple version of the divisor function we introduce a new zeta function which we call a multiple finite Riemann zeta function. We utilize some $q$-series identity for proving the zeta function has an Euler product and then,…

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

We prove the Riemann Hypothesis via an analytically regulated surface integral over the critical strip of the Riemann zeta function. The key idea is that the convergence of this normalized integral is equivalent to the condition that all…

We prove Riemann hypothesis. Method is to show the convexity of function which has zeros on open critical strip the same as zeta function.

Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the \emph{moment zeta function} of a probability distribution, and study in depth some asymptotic properties…

We prove that if a function $\theta \left( z \right)=\int\limits_{1}^{\infty }{\frac{\pi \left( t \right)\,-Li\left( t \right)}{{{t}^{z+1}}}dt}\,,$ which is holomorphic in $\left\{ \operatorname{Re}z>1 \right\}$ holomorphically extends to…

We present a proof of the functional equation of the Riemann zeta-function or more precisely the Dirichlet eta-function, which proof seems to be new but follows almost immediately from Malmst\`en's paper ``De integralibus quibusdam…

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…

The aim of this paper is to show further results following those published in [5], and to relate the Riemann zeta function to the relativistic cosmology.