Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis

2017/12/31 by Rubens Viana Ramos, R. V. Ramos, Ramos, R. V.
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications #math.GM #physics.gen-ph

paper · pdf · doi:10.48550/arxiv.1801.02459

15 pages. arXiv admin note: substantial text overlap with arXiv:1505.00741

arxiv created 2017/12/31 · arxiv updated 2018/01/09

Abstract

In the present work the Riemanns hypothesis (RH) is discussed from four different perspectives. In the first case, coherent states and the Stengers approximation to Riemann-zeta function are used to show that RH avoids an indeterminacy of the type 0/0 in the inner product of two coherent states. In the second case, the Hilber-Polya conjecture with a quantum circuit is considered. In the third case, randomness, entanglement and the Moebius function are used to discuss the RH. At last, in the fourth case, the RH is discussed by inverting the first derivative of the Chebyshev function. The results obtained reinforce the belief that the RH is true.

Citations

• Statistical and other properties of Riemann zeros based on an explicit equation for the n-th zero on the critical line
• Considerations about the randomness of bit strings originated from sequences of integer numbers according to a simple quantum computer model

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