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The Riemann Zeros as Spectrum and the Riemann Hypothesis [PDF]
Symmetry, 2016 We present a spectral realization of the Riemann zeros based on the propagation of a massless Dirac fermion in a region of Rindler spacetime and under the action of delta function potentials localized on the square free integers.
G. Sierra
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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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Colloquium: Physics of the Riemann hypothesis [PDF]
, 2011 Physicists become acquainted with special functions early in their studies. Consider our perennial model, the harmonic oscillator, for which we need Hermite functions, or the Laguerre functions in quantum mechanics.
Dániel Schumayer, D. A. W. Hutchinson
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On Robin's criterion for the Riemann Hypothesis
, 2006 Robin's criterion states that the Riemann Hypothesis (RH) is true if and only if Robin's inequality sum_{d|n}d=5041, where gamma denotes the Euler(-Mascheroni) constant.
YoungJu Choie +3 more
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Chebyshev's bias and generalized Riemann hypothesis [PDF]
, 2011 It is well known that $li(x)>\pi(x)$ (i) up to the (very large) Skewes' number $x_1 \sim 1.40 \times 10^{316}$ \cite{Bays00}. But, according to a Littlewood's theorem, there exist infinitely many $x$ that violate the inequality, due to the specific ...
Adel Alahmadi +2 more
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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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