Riemann Zeta Function Computed As 0 5 Yi Zi 3d Riemann Hypothesis PDF Download
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Author | : Jason Cole |
Publisher | : |
Total Pages | : 67 |
Release | : 2017-09-12 |
Genre | : |
ISBN | : 9781549727511 |
Download Riemann Zeta Function Computed As Ζ(0. 5+yi+zi) : 3D Riemann Hypothesis? Book in PDF, ePub and Kindle
In this book, I investigate (on a undergraduate level) a function similar to the Riemann zeta function, but with an additional free parameter: zeta(x+iy+iz), as a "3D" or "hyper-complex" zeta function. This researchstudies the analytic continuation of Zeta(1) and the zeros of this function, aiming to use this information to shed light on well-known problems in analytic number theory. Contained within this manuscript is a very short list of trivial zeros of zeta(x+yi+zi) to show data of how the trivial zeros form a discrete sawtooth Fourier wave in the 3D hypercomplex plane. The spectrum of a sawtooth wave mirrors the harmonic series. This research suggest that Zeta(1) is analytically continued into the rest of the complex plane as a discrete 3D sawtooth wave pattern made of trivial zeros. We can only observe the analytic continuation of Zeta(1) in the 3D hyper-complex plane as trivial zeros when Zeta is computed as s=x+yi+zi. This discovery of Zeta(1) analytically continued as the 3D trivial zeros (discrete sawtooth wave) suggest there is also a 3D hyper-complex landscape to the nontrivial zeros. A 3D or hyper-complex Riemann hypothesis were s=1/2+yi+zi. This book serves as the basis for 3D or hyper-complex analysis using computation were the Riemann Zeta function, similar L-functions, L-functions of Elliptic curves and Modular forms can be computed as s=x+yi+zi and give new insight into their properties that can't be seen when s=x+yi. This book also explore the topic of extending the Montgomery Pair correlation conjecture into the 3D or hyper-complex plane to correspond to the 3D or hyper-complex zeros of Riemann Zeta function.
Author | : S. J. Patterson |
Publisher | : Cambridge University Press |
Total Pages | : 172 |
Release | : 1995-02-02 |
Genre | : Mathematics |
ISBN | : 131658335X |
Download An Introduction to the Theory of the Riemann Zeta-Function Book in PDF, ePub and Kindle
This is a modern introduction to the analytic techniques used in the investigation of zeta functions, through the example of the Riemann zeta function. Riemann introduced this function in connection with his study of prime numbers and from this has developed the subject of analytic number theory. Since then many other classes of 'zeta function' have been introduced and they are now some of the most intensively studied objects in number theory. Professor Patterson has emphasised central ideas of broad application, avoiding technical results and the customary function-theoretic approach. Thus, graduate students and non-specialists will find this an up-to-date and accessible introduction, especially for the purposes of algebraic number theory. There are many exercises included throughout, designed to encourage active learning.
Author | : Peter B. Borwein |
Publisher | : Springer Science & Business Media |
Total Pages | : 543 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0387721258 |
Download The Riemann Hypothesis Book in PDF, ePub and Kindle
The Riemann Hypothesis has become the Holy Grail of mathematics in the century and a half since 1859 when Bernhard Riemann, one of the extraordinary mathematical talents of the 19th century, originally posed the problem. While the problem is notoriously difficult, and complicated even to state carefully, it can be loosely formulated as "the number of integers with an even number of prime factors is the same as the number of integers with an odd number of prime factors." The Hypothesis makes a very precise connection between two seemingly unrelated mathematical objects, namely prime numbers and the zeros of analytic functions. If solved, it would give us profound insight into number theory and, in particular, the nature of prime numbers. This book is an introduction to the theory surrounding the Riemann Hypothesis. Part I serves as a compendium of known results and as a primer for the material presented in the 20 original papers contained in Part II. The original papers place the material into historical context and illustrate the motivations for research on and around the Riemann Hypothesis. Several of these papers focus on computation of the zeta function, while others give proofs of the Prime Number Theorem, since the Prime Number Theorem is so closely connected to the Riemann Hypothesis. The text is suitable for a graduate course or seminar or simply as a reference for anyone interested in this extraordinary conjecture.
Author | : Edward Charles Titchmarsh |
Publisher | : Oxford University Press |
Total Pages | : 428 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 9780198533696 |
Download The Theory of the Riemann Zeta-function Book in PDF, ePub and Kindle
The Riemann zeta-function is our most important tool in the study of prime numbers, and yet the famous "Riemann hypothesis" at its core remains unsolved. This book studies the theory from every angle and includes new material on recent work.
Author | : Hugh Montgomery |
Publisher | : Springer |
Total Pages | : 300 |
Release | : 2017-09-11 |
Genre | : Mathematics |
ISBN | : 3319599690 |
Download Exploring the Riemann Zeta Function Book in PDF, ePub and Kindle
Exploring the Riemann Zeta Function: 190 years from Riemann's Birth presents a collection of chapters contributed by eminent experts devoted to the Riemann Zeta Function, its generalizations, and their various applications to several scientific disciplines, including Analytic Number Theory, Harmonic Analysis, Complex Analysis, Probability Theory, and related subjects. The book focuses on both old and new results towards the solution of long-standing problems as well as it features some key historical remarks. The purpose of this volume is to present in a unified way broad and deep areas of research in a self-contained manner. It will be particularly useful for graduate courses and seminars as well as it will make an excellent reference tool for graduate students and researchers in Mathematics, Mathematical Physics, Engineering and Cryptography.
Author | : Samuel W. Gilbert |
Publisher | : Riemann hypothesis |
Total Pages | : 160 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9781439216385 |
Download The Riemann Hypothesis and the Roots of the Riemann Zeta Function Book in PDF, ePub and Kindle
The author demonstrates that the Dirichlet series representation of the Riemann zeta function converges geometrically at the roots in the critical strip. The Dirichlet series parts of the Riemann zeta function diverge everywhere in the critical strip. It has therefore been assumed for at least 150 years that the Dirichlet series representation of the zeta function is useless for characterization of the non-trivial roots. The author shows that this assumption is completely wrong. Reduced, or simplified, asymptotic expansions for the terms of the zeta function series parts are equated algebraically with reduced asymptotic expansions for the terms of the zeta function series parts with reflected argument, constraining the real parts of the roots of both functions to the critical line. Hence, the Riemann hypothesis is correct. Formulae are derived and solved numerically, yielding highly accurate values of the imaginary parts of the roots of the zeta function.
Author | : S. J. Patterson |
Publisher | : Cambridge University Press |
Total Pages | : 176 |
Release | : 1995-02-02 |
Genre | : Mathematics |
ISBN | : 9780521499057 |
Download An Introduction to the Theory of the Riemann Zeta-Function Book in PDF, ePub and Kindle
An introduction to the analytic techniques used in the investigation of zeta functions through the example of the Riemann zeta function. It emphasizes central ideas of broad application, avoiding technical results and the customary function-theoretic appro
Author | : Harold M. Edwards |
Publisher | : |
Total Pages | : 315 |
Release | : 1974 |
Genre | : |
ISBN | : |
Download Riemann's zeta function Book in PDF, ePub and Kindle
Author | : Samuel Gilbert |
Publisher | : |
Total Pages | : 158 |
Release | : 2009-01-29 |
Genre | : |
ISBN | : 9781439226872 |
Download The Riemann Hypothesis and the Roots of the Riemann Zeta Function Book in PDF, ePub and Kindle
Author | : |
Publisher | : |
Total Pages | : 346 |
Release | : 1951 |
Genre | : |
ISBN | : |
Download The Theory of the Riemann Zeta-function Book in PDF, ePub and Kindle