FRACTAL SUPERSYMMETRIC QM, GEOMETRIC PROBABILITY AND THE RIEMANN HYPOTHESIS
نویسندگان
چکیده
منابع مشابه
Fractal supersymmetric QM, geometric probability and the Riemann hypothesis
The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. Earlier work on the RH based on supersymmetric QM, whose potential was related to the Gauss-Jacobi theta series, allows to provide the proper framework to construct the well defined algorithm to compute the probability to find a zero (an infinity of zeros) in the critical ...
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The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form sn = 1/2 + iλn. An improvement of our previous construction to prove the RH is presented by implementing the Hilbert-Polya proposal and furnishing the Fractal Supersymmetric Quantum Mechanical (SUSY-QM) model whose spectrum reproduces the imaginary parts of the zeta zeros. We model the fr...
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The Riemann’s hypothesis (RH) states that the nontrivial zeros of the Riemann zeta-function are of the form s = 1/2+iλn. Hilbert-Polya argued that if a Hermitian operator exists whose eigenvalues are the imaginary parts of the zeta zeros, λn’s, then the RH is true. In this paper a fractal supersymmetric quantum mechanical (SUSY-QM) model is proposed to prove the RH. It is based on a quantum inv...
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Associated to classical semi-simple groups and their maximal parabolics are genuine zeta functions. Naturally related to Riemann’s zeta and governed by symmetries, including that of Weyl, these zetas are expected to satisfy the Riemann hypothesis. For simplicity, G here denotes a classical semi-simple algebraic group defined over the field Q of rationals. With a fixed Borel, as usual, ∆0 stands...
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with s = 12 + it, and shows that ξ(t) is an even entire function of t whose zeros have imaginary part between −i/2 and i/2. He further states, sketching a proof, that in the range between 0 and T the function ξ(t) has about (T/2π) log(T/2π) − T/2π zeros. Riemann then continues “Man findet nun in der That etwa so viel reelle Wurzeln innerhalb dieser Grenzen, und es ist sehr wahrscheinlich, dass ...
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ژورنال
عنوان ژورنال: International Journal of Geometric Methods in Modern Physics
سال: 2004
ISSN: 0219-8878,1793-6977
DOI: 10.1142/s0219887804000393