The Riemann Hypothesis And The Roots Of The Riemann Zeta Function
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The Riemann Hypothesis And The Roots Of The Riemann Zeta Function
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Author : Samuel Gilbert
language : en
Publisher:
Release Date : 2009-01-29
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function written by Samuel Gilbert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-29 with categories.
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function
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Author : Samuel W. Gilbert
language : en
Publisher: Riemann hypothesis
Release Date : 2009
The Riemann Hypothesis And The Roots Of The Riemann Zeta Function written by Samuel W. Gilbert and has been published by Riemann hypothesis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
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.
Riemann S Zeta Function
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Author :
language : en
Publisher: Academic Press
Release Date : 1974-05-31
Riemann S Zeta Function written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974-05-31 with Mathematics categories.
RiemannÆs zeta function
The Riemann Hypothesis
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Author : Peter B. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008
The Riemann Hypothesis written by Peter B. Borwein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
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 Theory Of The Riemann Zeta Function
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Author : Edward Charles Titchmarsh
language : en
Publisher: Oxford University Press
Release Date : 1986
The Theory Of The Riemann Zeta Function written by Edward Charles Titchmarsh and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
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.
Riemann S Zeta Function
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Author : Harold M. Edwards
language : en
Publisher: Courier Corporation
Release Date : 2001-01-01
Riemann S Zeta Function written by Harold M. Edwards and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-01-01 with Mathematics categories.
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.
The Argument Of Mathematics
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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01
The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Exploring The Riemann Zeta Function
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Author : Hugh Montgomery
language : en
Publisher: Springer
Release Date : 2017-09-11
Exploring The Riemann Zeta Function written by Hugh Montgomery and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-11 with Mathematics categories.
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.
A Brief History Of Mathematics
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Author : Tianxin Cai
language : en
Publisher: Springer Nature
Release Date : 2023-07-25
A Brief History Of Mathematics written by Tianxin Cai and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-25 with Mathematics categories.
This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resulting applications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who's studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.
Unraveling The Enigma Of Riemann S Zeta Function A Journey Through The Realm Of Analytic Number Theory
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-10
Unraveling The Enigma Of Riemann S Zeta Function A Journey Through The Realm Of Analytic Number Theory written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-10 with Mathematics categories.
In the vast expanse of mathematical inquiry, few concepts have captured the imagination and ignited the curiosity of scholars like the Riemann zeta-function. Introduced by Bernhard Riemann in the 19th century, this enigmatic function has stood as a towering enigma, challenging mathematicians and inspiring generations of exploration. This comprehensive and engaging book invites you on an intellectual journey through the captivating world of the Riemann zeta-function, unveiling its intricate properties, profound applications, and historical significance. Delve into the depths of analytic number theory as we navigate concepts like Dirichlet's theorem, the prime number theorem, and the Riemann zeta-function's relationship with other mathematical functions. Unravel the mysteries surrounding the Riemann hypothesis, a conjecture that has captivated mathematicians for over a century. Discover the profound implications of this hypothesis, its potential to unlock the secrets of prime numbers, and its role in shaping our understanding of the fundamental nature of mathematics. Witness the Riemann zeta-function's remarkable applications in diverse fields, ranging from physics and computer science to finance and engineering. Explore its contributions to quantum field theory, string theory, coding theory, and cryptography, gaining insights into the function's versatility and far-reaching impact. Trace the Riemann zeta-function's historical significance, from its introduction by Riemann to its enduring legacy in modern mathematics. Learn about the brilliant minds who have dedicated their lives to studying this function, their contributions to the field, and the ongoing pursuit of knowledge that continues to drive research in this captivating area. Join us on this intellectual odyssey as we unravel the enigma of the Riemann zeta-function, embarking on an exploration that promises to expand your horizons, deepen your understanding of mathematics, and ignite your passion for discovery. Prepare to be captivated by the beauty, elegance, and profound implications of this mathematical marvel. If you like this book, write a review!