Related papers: Some possible approaches to the Riemann Hypothesis…
In this article we propose a revisitation of the well-known argument principle that may lead to the solution of the Riemann hypothesis. We are looking for collaborators.
The Keiper/Li constants $\{\lambda_n\}_{n=1,2,\ldots}$ are asymptotically ($n \to \infty$) sensitive to the Riemann Hypothesis, but highly elusive analytically and difficult to compute numerically. We present quite explicit variant…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
One of equivalents of the Riemann hypothesis is Li's criterion that all Li coefficients are positive. We study recurrence relations of Li coefficients in this note.
We substantially apply the Li criterion for the Riemann hypothesis to hold. Based upon a series representation for the sequence \{\lambda_k\}, which are certain logarithmic derivatives of the Riemann xi function evaluated at unity, we…
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
The Riemann hypothesis is equivalent to the Li criterion governing a sequence of real constants, that are certain logarithmic derivatives of the Riemann xi function evaluated at unity. We investigate a related set of constants c_n, n =…
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…
In this note, we give a simple proof that the Riemann Hypothesis is unprovable in any reasonable axiom system.
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. In particular, we argue that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ for $n \to…
A proposed solution to the Riemann Hypothesis
The transformations of the sum identities for generalized harmonic and oscillatory numbers, obtained earlier in our recent report [1], enable us to derive the new identities expressed in terms of the corresponding square roots of x. At…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
It is proposed that the validity, or not, of the Riemann Hypothesis might be established on the basis of the integral $$\int\frac{\xi(2s)}{\xi(s)}ds$$ where $$\xi(s)=(s-1)\pi^{-s/2}\Gamma(1+s/2)\zeta(s).$$
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.
In this paper we present an effective method for computing certain real coefficients $\lambda_{n}$ which appear in a criterion for the Riemann hypothesis proved by Xian-Jin Li. With the use of this method a sequence of over three-thousand…
The authors modify the Balazard-Saias criterion for the Riemann hypothesis by changing the cutoff of the Dirichlet series. They establish some asymptotic results related to the modified criterion.
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with…
A proof for the original Riemann hypothesis is proposed based on the infinite Hadamard product representation for the Riemann zeta function and later generalized to Dirichlet L-functions. The extension of the hypothesis to other functions…
In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure…