A quantum model of the distribution of prime numbers and the Riemann hypothesis

DOI10.1007/s10773-020-04512-2zbMath1441.82016OpenAlexW3041172755MaRDI QIDQ2197044

Vito Barbarani

Publication date: 4 September 2020

Published in: International Journal of Theoretical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10773-020-04512-2

zbMATH Keywords

quantum theoryRiemann hypothesisFibonacci numbersHellmann-Feynman theoremprime numbersnumber theory

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) Many-body theory; quantum Hall effect (81V70) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Distribution of primes (11N05) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Uses Software

• DLMF
• OEIS

Cites Work

• The prime-counting function and its analytic approximations. \(\pi(x)\) and its approximations
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• The \(n\)-th prime asymptotically
• A sharp region where 𝜋(𝑥)-𝑙𝑖(𝑥) is positive
• On the Difference π(x ) − lix (II)
• ON STRATEGIES TOWARDS THE RIEMANN HYPOTHESIS: FRACTAL SUPERSYMMETRIC QM AND A TRACE FORMULA
• A NEW BOUND FOR THE SMALLEST x WITH π(x) > li(x)
• Sharper Bounds for the Chebyshev Functions θ(x) and ψ(x). II
• A method for obtaining digital signatures and public-key cryptosystems
• The Riemann Zeros and Eigenvalue Asymptotics
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
• Statistics of Extremes
• A new bound for the smallest $x$ with $\pi(x) > \mathrm{li}(x)$
• QUANTUM HAMILTONIANS AND PRIME NUMBERS
• Forces in Molecules
• On the Distribution Function of the Remainder Term of the Prime Number Theorem
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