Preprint on ResearchGate.
ISSN/ISBN: Not available at this time. DOI: Not available at this time.
Abstract: The proof of Riemann’s hypothesis becomes simple by identifying the zeta function as the entropy of a number in which the real part is the integer and the imaginary part is the fraction. Since the entropy of a number is a sinusoidal wave, the zeta function is easily solved. We show that the Riemann zeta function is the Planck equation, in which the photon energy is a complex number. Further, it is argued that the zeros of the Riemann Zeta function are the resonances of the ground state of the quantum harmonic oscillator, where the photon energy is half-real and half-imaginary, namely, its energy is half-potential and half-kinetic. The real half of the oscillator energy is the 1⁄2 of the Riemann hypothesis. The imaginary part of the ground state is the resonance frequencies, which are the prime numbers. In the higher energy levels where the real energies are (n+1)/2, the imaginary resonance frequencies are the overtones. Since it was shown that the primes and their overtones include all the natural numbers, the zeros of the zeta function, which is the entropy of the quantum harmonic oscillator, are argued to be the generator of all the natural numbers.
Bibtex:
@misc{,
author = {Oded Kafri},
title = {The Columbus’s Egg of the Riemann Hypothesis},
year = {2025},
url = {https://www.researchgate.net/profile/Oded-Kafri/publication/390448474_ColumbusEgg/links/67ee3e2095231d5ba5ae4f4e/ColumbusEgg.pdf?__cf_chl_tk=GVf8DtJPMixzCGXAL_2BlFhCtSUMkbKkBOE_pSPaPI0-1745533161-1.0.1.1-Ub5lp9RFavrvXViLFge0mOV7yOynit0R0A76G6VookM},
}
Reference Type: Preprint
Subject Area(s): Number Theory, Physics