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Based on this approximation, we prove the Riemann hypothesis."K.

First published in Riemann's groundbreaking 1859 paper (Riemann 1859), the Riemann hypothesis is a deep mathematical conjecture which states that the nontrivial , i.e., the values of other than , , , ... such that (where is the ) all lie on the "" (where denotes the of ).

Bombieri, E.

Zerbini, (abstract) "We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis.

Clay Mathematics Institute. "The Riemann Hypothesis." .

Galetto,  (2014)[abstract:] "We show a proof of the so-called Riemann Hypothesis.

He worked with the Prime Number Theorem and Riemann's Hypothesis;and proved the unexpected fact that Chebyshev's bias, and, while true for most, and all butvery large, numbers, are violated infinitely often.

He introduced the Hilbert-Pólya Conjecture that theRiemann Hypothesis might be a consequence of spectral theory(in 2017 this Conjecture was partially proved by a team ofphysicists, and the Riemann Hypothesis be closeto solution!).

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

de Branges, L. "The Riemann hypothesis for Hilbert Spaces of Entire Functions." 15, 1-17, 1986.

In the novel (Jacoby 2008), the main character Theodore "Mead" Fegley (who is only 18 and a college senior) tries to prove the Riemann Hypothesis for his senior year research project. He also uses a Cray Supercomputer to calculate several billion zeroes of the Riemann zeta function. In several dream sequences within the book, Mead has conversations with Bernhard Riemann about the problem and mathematics in general.

The Riemann Hypothesis confirmation and its links to operators and random matrix theories are the direct mathematical implications of this bold view."


de Branges, L. "A Conjecture Which Implies the Riemann Hypothesis."  121, 117-184, 1994.
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Itallows to generalize the Riemann hypothesis to the reals.

Delille, who in 2004 began makingand retracting claims that he had a proof of the Riemann hypothesis,provided this , whichinvolves the analytic continuation of (August 2004).

The Riemann hypothesis is true according to the axiom.

Due to the importance of resolving the historical open natureof the Riemann hypothesis, comments by interested colleagues are here solicited."[]

and "Riemann Hypothesis." From --A Wolfram Web Resource.

Picard refutes Madrecki's proof

Jinzhu Han, Zaizhu Han, (06/2007)[abstract:] "In this paper, a proof of the Riemann Hypothesis is given.

I think this math has direct applicability to The Riemann Hypothesis.

Shi, (07/2003)[abstract:] "Beginning from the formal resolution of Riemann Zeta function, by using the formula of inner product between two infinite-dimensional vectors in the complex space, the author proved the world's baffling problem- Riemann hypothesis raised by German mathematician B.

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

In addition to simpler proofs of existing theorems, new theorems by Landauinclude important facts about Riemann's Hypothesis;facts about Dirichlet series;key lemmas of analysis;a result in Waring's Problem;a generalization of the Little Picard Theorem;a partial proof of Gauss' conjecture about the density of classesof composite numbers;and key results in the theory of pecking orders, e.g.

Several analogues of the Riemann hypothesis have already been proved

By constructing a continuous family of scaling-like operators involvingthe Gauss-Jacobi theta series, and by invoking a novel CT-invariantQuantum Mechanics, involving a judicious charge conjugation $C$and time reversal $T$ operation, we show why the Riemann Hypothesis is true."This follows earlier attempts:C.

Riemann Hypothesis not proved | The Aperiodical

Aizenberg, (12/2007)[abstract:] "We present an elementary, short and simple proof of the validity of the Lindelöf hypothesis about the Riemann zeta-function.

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