相关论文: On the Balazard-Saias criterion for the Riemann Hy…
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
In this paper we consider some possible approaches to the proof of the Riemann Hypothesis using the Li criterion.
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 the classical literature on infinite series there are various tests to determine if a given infinite series converges, diverges, or oscillates. But unfortunately, for very many infinite series all the existing tests can fail to provide…
We establish a new lower bound for Mathieu's series and present a new derivation of its expansions in terms of Riemann Zeta functions.
We investigate the relation between the Riesz and the Baez-Duarte criterion for the Riemann Hypothesis. In particular we present the relation between the function $R(x)$ appearing in the Riesz criterion and the sequence $c_k$ appearing in…
We investigate the relation between the Riesz and the B{\'a}ez-Duarte criterion for the Riemann Hypothesis. In particular we present the relation between the function $R(x)$ appearing in the Riesz criterion and the sequence $c_k$ appearing…
A crucial role in the Nyman-Beurling-B\'aez-Duarte approach to the Riemann Hypothesis is played by the distance \[ d_N^2:=\inf_{A_N}\frac{1}{2\pi}\int_{-\infty}^\infty\left|1-\zeta…
We establish sharp upper bounds for shifted moments of quadratic Dirichlet $L$-function under the generalized Riemann hypothesis. Our result is then used to prove bounds for moments of quadratic Dirichlet character sums.
We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(\Lambda-\lambda_k)_+^\sigma$ of the eigenvalues $\lambda_k$ of the Dirichlet Laplacian in a domain if $\sigma\geq 3/2$. It contains a correction term of the…
A proposed solution to the Riemann Hypothesis
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.
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…
Roy and Bhattacharya (2020) provided Bayesian characterization of infinite series, and their most important application, namely, to the Dirichlet series characterizing the (in)famous Riemann Hypothesis, revealed insights that are not in…
Conditionally on the Riemann hypothesis we prove asymptotic formulae for mean values of various long Dirichlet polynomials involving the von Mangoldt function. Our results avoid the use of correlation sum estimates although in addition to…
The achievement of this paper is a confutation of the inequality addressed by the Nicolas criterion for the Riemann Hypothesis, carried out after establishing properties of two related sequences. One of them is the product…
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.
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.
We extend Riemann's rearrangement theorem on conditionally convergent series of real numbers to multiple instead of simple sums.
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…