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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 ...
Alamadhi, Adel +2 more
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Two generalizations of Liouville λ function [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We study the properties of two classes of functions λₖ and ~λₖ that generalize the Liouville λ function, including some equivalencies between the Riemann hypothesis and some assertions about the asymptotic behavior of the summatory functions of λₖ and ...
André Pierro de Camargo
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The Generalized Riemann Hypothesis on elliptic complex fields
AIMS Mathematics, 2023 In this paper, we will introduce a new algebraic system called the elliptic complex, and consider the distribution of zeros of the function $ L(s, \chi) $ in the corresponding complex plane. The key to this article is to discover the limiting case of the
Xian Hemingway
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Black holes, quantum chaos, and the Riemann hypothesis
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 and Zeta-Function
Bibechana, 2018 No abstract available.
Mani Raj Bhattrai
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An Analytical and Numerical Detour for the Riemann Hypothesis
Information, 2021 From the functional equation F(s)=F(1−s) of Riemann’s zeta function, this article gives new insight into Hadamard’s product formula. The function S1(s)=d(lnF(s))/ds and its family of associated Sm functions, expressed as a sum of rational fractions, are ...
Michel Riguidel
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The Riemann hypothesis and tachyonic off-shell string scattering amplitudes
European Physical Journal C: Particles and Fields, 2022 The study of the $$\mathbf{4}$$ 4 -tachyon off-shell string scattering amplitude $$ A_4 (s, t, u) $$ A 4 ( s , t , u ) , based on Witten’s open string field theory, reveals the existence of poles in the s-channel and associated to a continuum of complex “
Carlos Castro Perelman
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Traces of certain integral operators related to the Riemann hypothesis
AIMS Mathematics, 2023 We prove the existence of a nontrivial singular trace $ \tau $ defined on an ideal $ \mathcal{J} $ closed with respect to the logarithmic submajorization such that $ \tau(A_\rho(\alpha)) = 0 $, where $ A_\rho(\alpha):L^{2}(0, 1)\to L^{2}(0, 1) $, $ {[A_ ...
Alfredo Sotelo-Pejerrey
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Toward the Unification of Physics and Number Theory [PDF]
Reports in Advances of Physical Sciences, 2019 This paper introduces the notion of simplex-integers and shows how, in contrast to digital numbers, they are the most powerful numerical symbols that implicitly express the information of an integer and its set theoretic substructure.
Klee Irwin
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Supersymmetry and the Riemann zeros on the critical line
Physics Letters B, 2019 We propose a new way of studying the Riemann zeros on the critical line using ideas from supersymmetry. Namely, we construct a supersymmetric quantum mechanical model whose energy eigenvalues correspond to the Riemann zeta function in the strip ...
Ashok Das, Pushpa Kalauni
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