Related papers: Some Sufficient Conditions for the Riemann hypothe…
In the paper, we first prove a sufficient condition for the Riemann hypothesis which involves the order of magnitude of the partial sum of the Liouville function. Then we show a formula which is curiously related to the proved sufficient…
We present a sufficient condition for the Riemann hypothesis. This condition is the existence of a special ordering on the set of finite products of distinct odd primes.
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.
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.
We provide new sufficient conditions under which Ryser's conjecture holds.
We present a simple proof of the Riemann's Hypothesis (RH) where only undergraduate mathematics is needed.
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
We give necessary and sufficient conditions for the Chebyshev inequality to be an equality.
This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the…
The Nyman-Beurling criterion, equivalent to the Riemann hypothesis (RH), is an approximation problem in the space of square integrable functions on $(0,\infty)$, involving dilations of the fractional part function by factors…
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…
In 1916, Riesz gave an equivalent criterion for the Riemann hypothesis (RH). Inspired from Riesz's criterion, Hardy and Littlewood showed that RH is equivalent to the following bound: \begin{align*} P_1(x):= \sum_{n=1}^\infty…
As essential condition for the validy of Robin's Theorem as a precondition for the proof of the Riemann hypothesis, we show that the minimum of the function $F={\rm e}^{\gamma}\,\ln(\ln\,n)-\sigma(n)/n$ is found to be positive. Therefore,…
The necessary and sufficient conditions for differentiability of a function of several real variables stated and proved and its ramifications discussed.
In the first part we present the number theoretical properties of the Riemann zeta function and formulate the Riemann Hypothesis. In the second part we review some physical problems related to this hypothesis: the links with Random Matrix…
Using two results of Garkavi, Medvedev and Khavinson, we give sufficient conditions for proximinality of sums of two ridge functions with bounded and continuous summands in the spaces of bounded and continuous multivariate functions…
The original criteria of Riesz and of Hardy-Littlewood concerning the truth of the Riemann Hypothesis (RH) are revisited and further investigated in light of the recent formulations and results of Maslanka and of Baez-Duarte concerning a…
This article contains work associated with a resolution of the Riemann hypothesis, following work by Taylor \cite{prt}, Lagarias and Suzuki \cite{lagandsuz} and Ki \cite{ki}, as well as Pustyl'nikov \cite{pust, pust2} and Keiper…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
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.