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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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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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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

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

Hardy–Littlewood–Riesz type equivalent criteria for the Generalized Riemann hypothesis [PDF]

Monatshefte für Mathematik (Print), 2022
In the present paper, we prove that the generalized Riemann hypothesis for the Dirichlet L -function $$L(s,\chi )$$ L ( s , χ ) is equivalent to the following bound: Let $$k \ge 1$$ k ≥ 1 and $$\ell $$ ℓ be positive real numbers.
Meghali Garg, B. Maji
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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

Riemann Hypothesis [PDF]

, 2023
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. Let's also define $S(x) = \theta(x) - x$, where $\theta(x)$ is the Chebyshev function.
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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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Supersymmetric quantum mechanics and the Riemann hypothesis [PDF]

International Journal of Modern Physics A, 2022
We construct a supersymmetric quantum mechanical model in which the energy eigenvalues of the Hamiltonians are the products of Riemann zeta functions. We show that the trivial and nontrivial zeros of the Riemann zeta function naturally correspond to the ...
Pushpa Kalauni, K. Milton
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