Itallows to generalize the Riemann hypothesis to the reals.

A proportionate operator is then constructed in a similar manner in terms of the non-trivial zeros of the Riemann zeta function, extending proportionately, mapping expectedly always to zero, which imposes a ratio of the primes to said zeta roots.

The Riemann hypothesis is true according to the axiom.

Galetto,  (2014)[abstract:]

The famous conjecture known as Riemann' s hypothesis

Does anyone know the current progress in showing the Riemann hypothesis? I was only able to find paper of Conrey that says at least 40% of the zeros of the Riemann Zeta function lie on the critical line.

The Riemann zeta function can also be defined in terms of by

The Riemann zeta function is an extremely important of mathematics and physics that arises in definite integration and is intimately related with very deep results surrounding the . While many of the properties of this function have been investigated, there remain important fundamental conjectures (most notably the ) that remain unproved to this day. The Riemann zeta function is defined over the complex plane for one complex variable, which is conventionally denoted (instead of the usual ) in deference to the notation used by Riemann in his 1859 paper that founded the study of this function (Riemann 1859). It is implemented in the as [].

Pozdnyakov,  (03/2012)[abstract:] "An equivalent formulation of the Riemann hypothesis is given.

Proof of the Riemann Hypothesis utilizing the theory …

Chengyan Liu, (09/1999)[abstract:] "Through an equivalent condition on the Farey series set forth by Franel and Landau, we prove Riemann Hypothesis for the Riemann zeta-function and the Dirichlet L-function.

Proof of the Riemann Hypothesis utilizing the

Huang, (purports to contain a sort of philosophical/psychological 'proof' of the RH)

The respected French economist Henri Berliocchi (who also seems to have extensive interests in homeopathy and mathematics) has brought out a book called (Economica, Paris, 2001: ISBN 2-7178342-6) in which he claimsto have disproved the Riemann Hypothesis.

Proposed (dis)proofs of the Riemann Hypothesis

As the founders of relevant logic, Anderson and Belnap, urge in their canonical book Entailment, a ‘proof’ submitted to a mathematics journal in which the essential steps fail to provide a reason to believe the conclusion, e.g. a proof by explosion, would be rejected out of hand. Mark Colyvan (2008) illustrates the point by noting that no one has laid claim to a startlingly simple proof of the Riemann hypothesis:

The important relationship between Riemann Hypothesis and random matrices was found by Freeman J.

Conrey, J. B. "The Riemann Hypothesis." 50,341-353, 2003. .

In addition to his own discoveries, Dirichlet played a key role ininterpreting the work of Gauss,and was an influential teacher,mentoring famous mathematicians likeBernhard Riemann (who considered Dirichlet second only to Gaussamong living mathematicians),Leopold Kronecker and Gotthold Eisenstein.

If the trace relation is satisfied this could be another test of the Riemann Hypothesis."A.

Weisstein, E. W. "Books about Riemann Zeta Function." .

He did very important work with prime numbers,proving that there is always a primebetween any and ,and working with the zeta function before Riemann did.

Thus, we provide evidence for the correctness of the Riemann Hypothesis."Loreno Heer comments "

Several analogues of the Riemann hypothesis have already been proved

Riemann’s Hypothesis: All the zeros of the zeta function have real part equal to > 1/2.
Proof: Let R stand for the Russell set, the set of all sets that are not members of themselves. It is straightforward to show that this set is both a member of itself and not a member of itself. Therefore, all the zeros of Riemann’s zeta function have real part equal to 1/2.