The Riemann Hypothesis states that the non-trivial zeros of the Zeta function all have real part one-half. The Hilbert-Polya conjecture states that the imaginary parts of the zeros of the Zeta function corresponds to eigenvalues of an unbounded self-adjoint operator. A (physical) refinement of it is the Berry-Keating conjecture, which is about a (supposed to be Hermitian!) Hamiltonian operator of a particle of mass that is moving under the influence of a potential.

Here we are (original version, August 2015)

July 2016 changes:  (1) Abstract   (2) summarizing lemmata D7-D11

Braun K., A Kummer function based Zeta function theory to prove the Riemann Hypothesis