Number Theory


Finding The Hamiltonian

Authors: Hung Tran

We first find a Hamiltonian H that has the Hurwitz zeta functions ζ(s,x) as eigenfunctions. Then we continue constructing an operator G that is self-adjoint, with appropriate boundary conditions. We will find that the ζ(s,x)-functions do not meet these boundary conditions, except for the ones where s is a nontrivial zero of the Riemann zeta, with the real part of s being greater than 1/2. Finally, we find that these exceptional functions cannot exist, proving the Riemann hypothesis, that all nontrivial zeros have real part equal to 1/2.

Comments: 5 Pages. Proof of the Riemann hypothesis using a Hamiltonian and a self-adjoint operator

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Submission history

[v1] 2019-06-24 20:24:24
[v2] 2019-06-25 11:55:41

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