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Prime Numbers And The Riemann Hypothesis PDF

Book Description:

Prime Numbers And The Riemann Hypothesis PDF

From the book cover you notice how Zeta ?(1/2+it) can be represented by a Parity Operator Wave function. This book is intended for a general audience but for Professional Mathematicians and Physicists the take away is that Zeta ?(1/2+it) is interpreted as a Parity Wave function and nontrivial zeros are zero probability locations over the reals. The wave curves of Zeta represent the atoms and the nontrivial zeros are interpreted as Zero probability. The atoms are repelling and not the zeros based on GUE. Within the context of Schrodinger equation the Hamiltonian Operator can be applied to the Parity wave function interpretation of Zeta to yield energy values associated to the Zeta function. By using a Parity wave function which is Hermitian can make the Zeta-Schrodinger equation yield real values. This Complex version of the Parity Operator wave function can mirror the wave graph of the Riemann Zeta function ?(½ + it)) to link the nontrivial zeros of Zeta to the eigenvalues of the Complex Parity wave function on the critical line as a new attack in proving RH. Using wave functions from Quantum mechanics the Riemann Zeta function and it’s nontrivial zeros can be recreated to Prove Riemann Hypothesis. The Riemann Hypothesis is a 160 yr. old mathematical problem. It concerns the roots(zeros) of a function called the Riemann Zeta function. The reason this function is so special is that it is related to the distribution of Prime Numbers and cryptography. The problem is so important that a Math institute have offered 1 million dollars to whoever can solve it. For the past 160 yrs. no one have been able to solve it using pure mathematics. However, a new physics discovery finally proves this Riemann Hypothesis. The discovery centers around using quantum mechanical wave functions and its eigenvalues to prove all the zeros(roots) of the Riemann Zeta function lie on a vertical line. This book reveals what may be the discovery of what type of self-adjoint operator the nontrivial Zeros are based upon to prove the Riemann Hypothesis. It is a Complex number version of the “Parity Operator”. The conjecture is that the nontrivial zeros are based on a Complex Number version of the Parity Operator. The Zeta function graph ?(½ + it)) is a wave function ? and that is how the nontrivial zeros have eigenvalues properties. The Real R(?(½ + it)) and imaginary part I(?(½ + it)) of the Zeta function are based on Even Parity and odd Parity wave functions. The Parity Parity Operator precisely describe the energy levels inside big atomic nuclei. Mathematically the Parity Operator is a real function and defined as P ?(x) = +1? (-x) for it’s Even Parity and P? (x) = -1? (-x) for Odd Parity. I am correlating R(?(0.5+it)) = R(?(0.5- it)) to the Even Parity P ?(x) = +1? (-x) and I(?(0.5+it)) = -I(?(0.5-it)) to P? (x) = -1? (-x) as the basis for a new Complex Parity Operator whose spectrum equal the nontrivial zeros of the Zeta function. In which ?(0.5+it)) is interpreted as a wave function ? and that is what’s giving the nontrivial zeros it’s eigenvalue. The New Parity Operator has a Euler Product. Just as Zeta ?(½ + it) and PSI ?(1/2 +it) can equal, the new Complex Parity functional equation that mirrors Zeta functional equation can also equal Zeta for values greater than 1 over reals. The core concept of this book can be found on an archive as a 4 page manuscript. The title of the paper is “The wave function ? of the Riemann Zeta function”. It is posted on Vixra for the purpose of giving others the copyright license freedom to share the work(pdf). This work just like any other work always need to be peer-reviewed and the benefit of posting it on Vixra is that it clears up copyright complications so others can share, report and peer-review it. The Vixra link is as follows: http://vixra.org/abs/1705.0117?.

Book Details:

Prime Numbers And The Riemann Hypothesis PDF

Author Jason Cole
Isbn 1542967252
File size 20.9 MB
Year 2017
Pages 249
Language English
File format PDF
Category Mathematics
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