The Quantized Constants with Remmen’s Scattering Amplitude to Explain Riemann Zeta Zeros

Abstract

Riemann Hypothesis has been proposed by Bernhard Riemann since year 1859. Nowadays, there are lots of proof or disproof all over the internet society or the academic professional authority etc. However, none of them is accepted by the Clay’s Mathematics Institute for her Millennium Prize. In the past few months, this author discovered that there may be a correlation exists between the real and imaginary parts of Riemann Zeta function for the first 10 non-trivial zeros of the Riemann function etc. Indeed, when one tries to view the correlation relationship as a constant like the Planck’s one. Then we may show that Riemann Zeta zeros are indeed discrete quantum energy levels or the discrete spectrum as electrons falling from some bound quantum state to a lower energy state (or Quantum Field Theory). That may be further explained by Remmen’s scattering amplitude or the S-matrix. We may approximate the S-matrix by applying the HKLam theory to it and predict the scattering amplitude or even the Riemann Zeta non-trival zeros etc. By the way, the key researching equations or formula in the following content will be around the Taylor expansion of the Riemann Zeta function, their convergence etc. In additional, I will also investigate the (*’’) as shown below: ∏_(i=1)^∞▒(z-z_i ) = ξ(0.5 + i*t) = (∑_(n=1)^∞▒1)⁄n^((0.5+i*t) ) = ∏_(j=1)^∞▒(1-1⁄(p_j^((0.5+i*t) ) ))^(-1) ------------ (*’’) as we may find the existence of some constants like the Planck’s one. For the application of the aforementioned scholarly outcome, it is well-known that if one can find the pattern of the appearance to the prime number and hence break the public key cryptography in the everyday usage of information technology security etc.