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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. All attempts failed so far to represent the Riemann duality equation in the critical stripe as convergent (!) Mellin transforms of an underlying self adjoint integral equation relation.The idea of our two proofs of the RH is to build such a self adjoint integral equation relation in a weak distribution sense only, built on an appropriately defined inner product. This is the prize to be paid for the convergent Mellin transforms. Spectral analysis can then be applied to answer the RH positively in a weak sense. With standard density arguments then it gives the RH also in a strong sense. Acknowledgement I want to express my deep thanks to those people from academical world, who made the paradigma change happen, publishing academical research results on internet to share it to the whole public community. Many thanks therefore especially to all authors of the references in this domain. Without them this domain never would have been launched. A special thank you to the following great institution http://www.digizeitschriften.de As a introductions to the Riemann Hypothesis we refer to
and just for fun:
Pls. note, that there are some errors mentioned in H.M. Edwards, Riemann´s Zeta function, e.g. chapter 1.16 This domain also contains an idea to prove that Euler´s Gamma constant is irrational. Some ideas about an alternative mathematical framework to model quantum gravitation theory is given @ |
