On the Non-trivial Zeta Zeroes and its significance in Quantum Systems
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چکیده
Motivated by Hilbert and Pölya, there were many developments in the field of spectral theory related to the study of Riemann’s Zeta zeroes. In this paper, Riemann’s 1859 paper is discussed, deriving the formula for the prime counting function that Riemann obtained. Another formula due to Weil will also be derived. The line of development of classical mechanics to quantum mechanics were presented and Floquet operator of periodic Hamiltonian was discussed and used in the kicked rotator model. A brief layout of using trace Green’s function to determine the density of state was carried out and the Gutzwiller’s trace formula was quoted. Functional Equation of ζ The zeta function, ζ(s) defined for Re(s) > 1 is given by ζ(s) = ∑
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تاریخ انتشار 2009