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Title:
The argument of the completed zeta function: From the computation of very high zeros to the Quantum Hall effect.
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Abstract:
This talk naturally separates into two distinct parts, though both parts are based on the argument of the completed zeta function $\pi^{-s/2} \Gamma(s/2) \zeta (s)$. The first part deals with an exact transcendental equation satisfied by individual zeros on the critical line, which depends only on the zero number, i.e. the integer that enumerates the zeros. Combined with the Euler product formula we can calculate very high zeros, in particular the google-th zero, to a certain degree of accuracy depending on home many primes are kept in the Euler product. In the second part we will use the same function to propose a phenomenological formula for the transverse resistivity in the Quantum Hall effect. We describe the consequences of the Riemann Hypothesis for this hypothetical formula. We also argue that the random properties of the zeros arise from the disordered landscape experienced by the electrons, again assuming our phenomenological formula.
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