Equivalents Of The Riemann Hypothesis Volume 3 Further Steps Towards Resolving The Riemann Hypothesis
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Equivalents Of The Riemann Hypothesis Volume 3 Further Steps Towards Resolving The Riemann Hypothesis
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Author : Kevin Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2023-10-12
Equivalents Of The Riemann Hypothesis Volume 3 Further Steps Towards Resolving The Riemann Hypothesis written by Kevin Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-12 with Mathematics categories.
The Riemann hypothesis (RH) may be the most important outstanding problem in mathematics. This third volume on equivalents to RH comprehensively presents recent results of Nicolas, Rogers–Tao–Dobner, Polymath15, and Matiyasevich. Particularly interesting are derivations which show, assuming all zeros on the critical line are simple, that RH is decidable. Also included are classical Pólya–Jensen equivalence and related developments of Ono et al. Extensive appendices highlight key background results, most of which are proved. The book is highly accessible, with definitions repeated, proofs split logically, and graphical visuals. It is ideal for mathematicians wishing to update their knowledge, logicians, and graduate students seeking accessible number theory research problems. The three volumes can be read mostly independently. Volume 1 presents classical and modern arithmetic RH equivalents. Volume 2 covers equivalences with a strong analytic orientation. Volume 3 includes further arithmetic and analytic equivalents plus new material on RH decidability.
Equivalents Of The Riemann Hypothesis
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Author : Kevin Alfred Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2017
Equivalents Of The Riemann Hypothesis written by Kevin Alfred Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Riemann hypothesis categories.
This three-volume work presents the main known equivalents to the Riemann hypothesis, perhaps the most important problem in mathematics. Volume 3 covers new arithmetic and analytic equivalences from numerous studies in the field, such as Rogers and Tao, and presents derivations which show whether the Riemann hypothesis is decidable.
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.
Equivalents Of The Riemann Hypothesis
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Author : Kevin Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-02
Equivalents Of The Riemann Hypothesis written by Kevin Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-02 with Mathematics categories.
This second volume of two presents analytic equivalents to the Riemann hypothesis. Includes an extensive set of appendices.
Prime Numbers And The Riemann Hypothesis
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Author : Barry Mazur
language : en
Publisher: Cambridge University Press
Release Date : 2016-04-11
Prime Numbers And The Riemann Hypothesis written by Barry Mazur and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-11 with Mathematics categories.
This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.
Mathematics And Computation
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Author : Avi Wigderson
language : en
Publisher: Princeton University Press
Release Date : 2019-10-29
Mathematics And Computation written by Avi Wigderson and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-29 with Computers categories.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophy Mathematics and Computation provides a broad, conceptual overview of computational complexity theory—the mathematical study of efficient computation. With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors. Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered. Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography
Equivalents Of The Riemann Hypothesis Volume 2 Analytic Equivalents
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Author : Kevin Broughan
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-02
Equivalents Of The Riemann Hypothesis Volume 2 Analytic Equivalents written by Kevin Broughan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-02 with Mathematics categories.
The Riemann hypothesis (RH) is perhaps the most important outstanding problem in mathematics. This two-volume text presents the main known equivalents to RH using analytic and computational methods. The book is gentle on the reader with definitions repeated, proofs split into logical sections, and graphical descriptions of the relations between different results. It also includes extensive tables, supplementary computational tools, and open problems suitable for research. Accompanying software is free to download. These books will interest mathematicians who wish to update their knowledge, graduate and senior undergraduate students seeking accessible research problems in number theory, and others who want to explore and extend results computationally. Each volume can be read independently. Volume 1 presents classical and modern arithmetic equivalents to RH, with some analytic methods. Volume 2 covers equivalences with a strong analytic orientation, supported by an extensive set of appendices containing fully developed proofs.
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.
Elementary Number Theory Primes Congruences And Secrets
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Author : William Stein
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-28
Elementary Number Theory Primes Congruences And Secrets written by William Stein 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 2008-10-28 with Mathematics categories.
This is a book about prime numbers, congruences, secret messages, and elliptic curves that you can read cover to cover. It grew out of undergr- uate courses that the author taught at Harvard, UC San Diego, and the University of Washington. The systematic study of number theory was initiated around 300B. C. when Euclid proved that there are in?nitely many prime numbers, and also cleverly deduced the fundamental theorem of arithmetic, which asserts that every positive integer factors uniquely as a product of primes. Over a thousand years later (around 972A. D. ) Arab mathematicians formulated the congruent number problem that asks for a way to decide whether or not a given positive integer n is the area of a right triangle, all three of whose sides are rational numbers. Then another thousand years later (in 1976), Di?e and Hellman introduced the ?rst ever public-key cryptosystem, which enabled two people to communicate secretely over a public communications channel with no predeterminedsecret; this invention and the ones that followed it revolutionized the world of digital communication. In the 1980s and 1990s, elliptic curves revolutionized number theory, providing striking new insights into the congruent number problem, primality testing, publ- key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles’ resolution of Fermat’s Last Theorem.
The Riemann Zeta Function
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Author : Aleksandar Ivic
language : en
Publisher: Courier Corporation
Release Date : 2012-07-12
The Riemann Zeta Function written by Aleksandar Ivic and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-07-12 with Mathematics categories.
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.