Results 11 to 20 of about 1,625,058 (297)

Riemann hypothesis

Journal of Applied Mathematics and Physics, 2019
This work is dedicated to the promotion of the results Hadamard, Landau E., Walvis A., Estarmann T and Paul R. Chernoff for pseudo zeta functions.
Durmagambetov, A.
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An essay on the Riemann Hypothesis [PDF]

, 2015
The Riemann hypothesis is, and will hopefully remain for a long time, a great motivation to uncover and explore new parts of the mathematical world. After reviewing its impact on the development of algebraic geometry we discuss three strategies, working ...
Connes Alain
semanticscholar   +5 more sources

The Riemann Hypothesis

Explorations in Complex Functions, 2020
Let's define $\delta(x) = (\sum_{{q\leq x}}{\frac{1}{q}}-\log \log x-B)$, where $B \approx 0.2614972128$ is the Meissel-Mertens constant. The Robin theorem states that $\delta(x)$ changes sign infinitely often.
F. Vega
semanticscholar   +3 more sources

Thoughts on the Riemann hypothesis [PDF]

The Mathematical Intelligencer, 2003
The simultaneous appearance in May 2003 of four books on the Riemann hypothesis (RH) provoked these reflections. We briefly discuss whether the RH should be added as a new axiom, or whether a proof of the RH might involve the notion of ...
Chaitin, G. J.
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The Riemann Hypothesis [PDF]

arXiv, 2007
The Riemann Hypothesis is a conjecture made in 1859 by the great mathematician Riemann that all the complex zeros of the zeta function $\zeta(s)$ lie on the `critical line' ${Rl} s= 1/2$. Our analysis shows that the assumption of the truth of the Riemann Hypothesis leads to a contradiction.
arxiv   +3 more sources

BOUNDING ZETA ON THE 1-LINE UNDER THE PARTIAL RIEMANN HYPOTHESIS [PDF]

Bulletin of the Australian Mathematical Society, 2023
We provide explicit bounds for the Riemann zeta-function on the line $\mathrm {Re}\,{s}=1$ , assuming that the Riemann hypothesis holds up to height T.
Andrés Chirre
semanticscholar   +1 more source

The Generalized Riemann Hypothesis from zeros of the zeta function [PDF]

Research in Number Theory, 2023
We show that the Generalized Riemann Hypothesis for all Dirichlet L-functions is a consequence of certain conjectural properties of the zeros of the Riemann zeta function.
W. Banks
semanticscholar   +1 more source

Chebyshev’s bias for Ramanujan’s $\tau$-function via the Deep Riemann Hypothesis [PDF]

Proceedings of the Japan Academy. Series A Mathematical sciences, 2022
The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan’s τ -function has a bias to being positive. This phenomenon is an analogue of Chebyshev’s bias.
S. Koyama, N. Kurokawa
semanticscholar   +1 more source

Towards the Generalized Riemann Hypothesis using only zeros of the Riemann zeta function [PDF]

Research in Number Theory, 2022
For any real $$\beta _0\in [\tfrac{1}{2},1)$$ β 0 ∈ [ 1 2 , 1 ) , let $$\textrm{GRH}[\beta _0]$$ GRH [ β 0 ] be the assertion that for every Dirichlet character $$\chi $$ χ and all zeros $$\rho =\beta +i\gamma $$ ρ = β + i γ of $$L(s,\chi )$$ L ( s , χ )
W. Banks
semanticscholar   +1 more source

Improving bounds on prime counting functions by partial verification of the Riemann hypothesis [PDF]

The Ramanujan journal, 2021
Using a recent verification of the Riemann hypothesis up to height 3·1012\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek ...
Daniel R. Johnston
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