Exploring the Riemann Zeta Function

Exploring the Riemann Zeta Function PDF

Author: Hugh Montgomery

Publisher: Springer

Published: 2017-09-11

Total Pages: 298

ISBN-13: 3319599690

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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.

Riemann's Zeta Function

Riemann's Zeta Function PDF

Author: Harold M. Edwards

Publisher: Courier Corporation

Published: 2001-01-01

Total Pages: 338

ISBN-13: 9780486417400

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Superb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix.

Lectures on the Riemann Zeta Function

Lectures on the Riemann Zeta Function PDF

Author: H. Iwaniec

Publisher: American Mathematical Society

Published: 2014-10-07

Total Pages: 130

ISBN-13: 1470418517

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The Riemann zeta function was introduced by L. Euler (1737) in connection with questions about the distribution of prime numbers. Later, B. Riemann (1859) derived deeper results about the prime numbers by considering the zeta function in the complex variable. The famous Riemann Hypothesis, asserting that all of the non-trivial zeros of zeta are on a critical line in the complex plane, is one of the most important unsolved problems in modern mathematics. The present book consists of two parts. The first part covers classical material about the zeros of the Riemann zeta function with applications to the distribution of prime numbers, including those made by Riemann himself, F. Carlson, and Hardy-Littlewood. The second part gives a complete presentation of Levinson's method for zeros on the critical line, which allows one to prove, in particular, that more than one-third of non-trivial zeros of zeta are on the critical line. This approach and some results concerning integrals of Dirichlet polynomials are new. There are also technical lemmas which can be useful in a broader context.

The Riemann Zeta-Function

The Riemann Zeta-Function PDF

Author: Aleksandar Ivic

Publisher: Courier Corporation

Published: 2012-07-12

Total Pages: 548

ISBN-13: 0486140040

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This text covers exponential integrals and sums, 4th power moment, zero-free region, mean value estimates over short intervals, higher power moments, omega results, zeros on the critical line, zero-density estimates, and more. 1985 edition.

The Riemann Hypothesis

The Riemann Hypothesis PDF

Author: Peter B. Borwein

Publisher: Springer Science & Business Media

Published: 2008

Total Pages: 543

ISBN-13: 0387721258

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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.

The Riemann Hypothesis and the Distribution of Prime Numbers

The Riemann Hypothesis and the Distribution of Prime Numbers PDF

Author: Naji Arwashan, PhD, PE

Publisher: Nova Science Publishers

Published: 2021-04-15

Total Pages: 232

ISBN-13: 1536194220

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This book is an introductory and comprehensive presentation of the Riemann Hypothesis, one of the most important open questions in math today. It is introductory because it is written in an accessible and detailed format that makes it easy to read and understand. And it is comprehensive because it explains and proves all the mathematical ideas surrounding and leading to the formulation of the hypothesis.

Stalking the Riemann Hypothesis

Stalking the Riemann Hypothesis PDF

Author: Dan Rockmore

Publisher: Vintage

Published: 2006-05-09

Total Pages: 306

ISBN-13: 0375727728

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For 150 years the Riemann hypothesis has been the holy grail of mathematics. Now, at a moment when mathematicians are finally moving in on a proof, Dartmouth professor Dan Rockmore tells the riveting history of the hunt for a solution.In 1859 German professor Bernhard Riemann postulated a law capable of describing with an amazing degree of accuracy the occurrence of the prime numbers. Rockmore takes us all the way from Euclid to the mysteries of quantum chaos to show how the Riemann hypothesis lies at the very heart of some of the most cutting-edge research going on today in physics and mathematics.

Riemann Zeta Function Computed As Ζ(0. 5+yi+zi): 3D Riemann Hypothesis

Riemann Zeta Function Computed As Ζ(0. 5+yi+zi): 3D Riemann Hypothesis PDF

Author: Jason Cole

Publisher:

Published: 2017-11-23

Total Pages: 129

ISBN-13: 9781973372585

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In this book, I investigate (on a undergraduate level) the implication of 3D nontrivial zero solutions and its connection to the Montgomery Pair correlation conjecture. If their exist a 3D landscape to the nontrivial zeros (3D Riemann Hypothesis) then correspondingly their exist a 3D eigenvalue landscape. The arrangement of these 3D hypercomplex eigenvalue equivalent to 3D hypercomplex nontrivial zero solutions. What makes this so interesting is that this 3D eigenvalue landscape may be describing a new undiscovered 3D hypercomplex Quantum Mechanical landscape. I also explore other new discoveries on L-functions and the Prime Number Theorem.

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