Black holes, quantum chaos, and the Riemann hypothesis [PDF]
SciPost Physics Core, 2021 Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for
Panagiotis Betzios, Nava Gaddam, Olga Papadoulaki
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Riemann hypothesis for period polynomials of modular forms. [PDF]
Proc Natl Acad Sci U S A, 2016 Significance Critical values of modular L-functions are objects of central importance in arithmetic geometry and number theory. These numbers are predicted to encode deep arithmetic information by the Birch and Swinnerton-Dyer conjecture and the Bloch ...
Jin S, Ma W, Ono K, Soundararajan K.
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New versions of the Nyman-Beurling criterion for the Riemann hypothesis [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 Let ρ(x)=x−[x], χ=χ(0,1), λ(x)=χ(x)logx, and M(x)=ΣK≤x μ(k), where μ is the Möbius function.
Luis Báez-Duarte
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Variants on Andrica’s Conjecture with and without the Riemann Hypothesis [PDF]
Mathematics, 2018 The gap between what we can explicitly prove regarding the distribution of primes and what we suspect regarding the distribution of primes is enormous. It is (reasonably) well-known that the Riemann hypothesis is not sufficient to prove Andrica’s ...
Matt Visser
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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
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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
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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
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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
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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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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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