Related papers: On the Riemann Hypothesis
In this paper, we derive $C^2$ estimates for a class of mixed Hessian type equations with Dirichlet boundary condition, and obtain the existence theorem of admissible solutions for the classical Dirichlet problem of these mixed Hessian type…
In this work we consider an equation for the Riemann zeta-function in the critical half-strip. With the help of this equation we prove that finding non-trivial zeros of the Riemann zeta-function outside the critical line would be equivalent…
A recent problem [B. Gardas, J. Math. Phys. 52, 042104 (2011)] concerning an antilinear solution of the Riccati equation is solved. We also exemplify that a simplification of the Riccati equation, even under reasonable assumptions, can lead…
The Riemann hypothesis, stating that the real part of all non-trivial zero points fo the zeta function must be $\frac{1}{2}$, is one of the most important unproven hypothesises in number theory. In this paper we will proof the Riemann…
In this paper a new integral for the remainder of $\pi(x)$ is obtained. It is proved that there is an infinite set of the formulae containing miscellaneous parts of this integral.
This review article brings forth some recent results in the theory of the Riemann zeta-function $qzeta(s)$.
In this article, we establish an asymptotic formula for the eighth moment of the Riemann zeta function, assuming the Riemann hypothesis and a quaternary additive divisor conjecture. This builds on the work of the first author on the sixth…
Baez-Duarte reformulated the Riemann hypothesis as a statement about a Hilbert space distance, involving the integer dilations of the "fractional part" function. Under the assumption of the Riemann hypothesis, we improve on the currently…
In this note we obtain a new convergence result for the Adomian decomposition method.
We study multi-phase Stefan problem with increasing Riemann initial data and with generally negative latent specific heats for the phase transitions. We propose the variational formulation of self-similar solutions, which allows to find…
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.
This paper is a summary of the general approach outlined in my previous papers toward proving the riemann hypothesis. Numerical and graphical proof of the Riemann Hypothesis is presented with analytical arguments although more work needs…
We prove several extensions of the Erdos-Fuchs theorem.
This paper is a continuation of our recent paper with the same title, arXiv:0806.1596v1 [math.NT], where a number of integral equalities involving integrals of the logarithm of the Riemann zeta-function were introduced and it was shown that…
We generalize some classical results for the Schlesinger system of partial differential equations and give the explicit form of its solution, associated with rational matrix functions in general position.
The Alternative Hypothesis concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between nontrivial zeros…
We present a conjecture about the asymptotic representation of certain series. The conjecture implies the Riemann hypothesis and it would also indicate the simplicity of the non-trivial zeros of the zeta-function.
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…
This paper has been withdrawn by the author, due to a crucial error in page 5.
We provide elementary and accurate numerical solutions to the differential-difference equation, which improves an explicit version of the linear sieve given by Nathanson.