The Riemann Hypothesis And The Distribution Of Prime Numbers
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The Riemann Hypothesis And The Distribution Of Prime Numbers
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Author : Naji Arwashan, PhD, PE
language : en
Publisher: Nova Science Publishers
Release Date : 2021-04-15
The Riemann Hypothesis And The Distribution Of Prime Numbers written by Naji Arwashan, PhD, PE and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-15 with Mathematics categories.
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.
The Distribution Of Prime Numbers
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Author : Albert Edward Ingham
language : en
Publisher: Cambridge University Press
Release Date : 1990-09-28
The Distribution Of Prime Numbers written by Albert Edward Ingham 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 1990-09-28 with Mathematics categories.
Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.
The Riemann Hypothesis
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Author : Peter Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-21
The Riemann Hypothesis written by Peter 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 2007-11-21 with Mathematics categories.
This book presents the Riemann Hypothesis, connected problems, and a taste of the body of theory developed towards its solution. It is targeted at the educated non-expert. Almost all the material is accessible to any senior mathematics student, and much is accessible to anyone with some university mathematics. The appendices include a selection of original papers that encompass the most important milestones in the evolution of theory connected to the Riemann Hypothesis. The appendices also include some authoritative expository papers. These are the “expert witnesses” whose insight into this field is both invaluable and irreplaceable.
Entangling Primes And Zeros
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Author : David R Ely
language : en
Publisher: David R Ely
Release Date : 2024-04-26
Entangling Primes And Zeros written by David R Ely and has been published by David R Ely this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-26 with Mathematics categories.
For over 150 years, the Riemann Hypothesis stood as perhaps the greatest unsolved problem in mathematics. Proposed in 1859 by Bernard Riemann, the conjecture provided a tantalizing connection between the distribution of prime numbers and the zeros of an analytic function. Riemann located all the non-trivial zeros of the zeta function along a straight line in the complex plane. This simple pattern pointed to hidden order in the chaos of prime numbers. Generations of mathematicians struggled in vain to prove Riemann's alluring claim. It became the holy grail of number theory, resisting the most powerful mathematical minds. The Riemann Hypothesis gained renown as the most important problem in all of mathematics. But despite intense effort, the problem seemed mired in insurmountable difficulty. In this book, we walk through the proof that could finally cracked Riemann's age-old enigma. By bringing together ideas from complex analysis, number theory, and topology, the proof provides a creative bridge between mathematics' disparate domains. Methods based on symmetry, contradiction, and strategic re-expression illuminate Riemann's magic at last. The book offers the first comprehensive guide to understanding and appreciating this watershed mathematical achievement. It provides deep mathematical insights, historical perspectives, and reflection on problem-solving philosophy. Most importantly, the work pays tribute to the human spirit embodied in mathematics’ unending quest to understand the mysteries of patterns that surround us.
The Symphony Of Primes Distribution Of Primes And Riemann S Hypothesis
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Author : Jan Feliksiak
language : en
Publisher: Xlibris Corporation
Release Date : 2013-03-14
The Symphony Of Primes Distribution Of Primes And Riemann S Hypothesis written by Jan Feliksiak and has been published by Xlibris Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Education categories.
This book presents research results concerning the distribution of prime numbers. The first major result discussed is the supremum for the maximal prime gaps. By an implementation of a binomial coefficient the maximal prime gaps supremum bound is proved, simultaneously establishing the infimum for primes in the short interval. Subsequently, a novel application of the theory of the primorial function establishes the tailored logarithmic integral, which is a superior adaptation of the classical Gauss' logarithmic integral. The tailored integral due to its radically improved accuracy over the Gauss' logarithmic integral, constitutes the supremum bound of estimation of the prime counting function. It presents the possibility to estimate the prime counting function with unprecedented accuracy.
The Prime Numbers And Their Distribution
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Author : Gerald Tenenbaum
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
The Prime Numbers And Their Distribution written by Gerald Tenenbaum and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
One notable new direction this century in the study of primes has been the influx of ideas from probability. The goal of this book is to provide insights into the prime numbers and to describe how a sequence so tautly determined can incorporate such a striking amount of randomness. The book opens with some classic topics of number theory. It ends with a discussion of some of the outstanding conjectures in number theory. In between are an excellent chapter on the stochastic properties of primes and a walk through an elementary proof of the Prime Number Theorem. This book is suitable for anyone who has had a little number theory and some advanced calculus involving estimates. Its engaging style and invigorating point of view will make refreshing reading for advanced undergraduates through research mathematicians.
The Distribution Of Prime Numbers
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Author : Dimitris Koukoulopoulos
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-28
The Distribution Of Prime Numbers written by Dimitris Koukoulopoulos and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-28 with Education categories.
Prime numbers have fascinated mathematicians since the time of Euclid. This book presents some of our best tools to capture the properties of these fundamental objects, beginning with the most basic notions of asymptotic estimates and arriving at the forefront of mathematical research. Detailed proofs of the recent spectacular advances on small and large gaps between primes are made accessible for the first time in textbook form. Some other highlights include an introduction to probabilistic methods, a detailed study of sieves, and elements of the theory of pretentious multiplicative functions leading to a proof of Linnik's theorem. Throughout, the emphasis has been placed on explaining the main ideas rather than the most general results available. As a result, several methods are presented in terms of concrete examples that simplify technical details, and theorems are stated in a form that facilitates the understanding of their proof at the cost of sacrificing some generality. Each chapter concludes with numerous exercises of various levels of difficulty aimed to exemplify the material, as well as to expose the readers to more advanced topics and point them to further reading sources.
Riemann Hypothesis And The Prime Representing Constant
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Author : Angeles Guro Bulanhagui
language : en
Publisher: Independently Published
Release Date : 2022-10-23
Riemann Hypothesis And The Prime Representing Constant written by Angeles Guro Bulanhagui and has been published by Independently Published this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-23 with categories.
The Riemann Zeta Function is a function in analytical number theory, that has a connection to the distribution of prime numbers. The Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part 1/2. Using these properties, we unveil the mystery of prime numbers.
The Mathematics Of Pi And The Riemann Hypothesis
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Author : Ryaed Owens
language : en
Publisher:
Release Date : 2024-09-23
The Mathematics Of Pi And The Riemann Hypothesis written by Ryaed Owens and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Education categories.
The Riemann hypothesis is an unsolved problem regarding the distribution of prime numbers that was first penned by Bernhard Riemann in 1859 and continues to perplex mathematicians today. Riemann built on previous work by Leonhard Euler on the connection between the zeta function and the distribution of prime numbers.In this study, Ryaed Owens advances the study of the zeta function and Euler's product formula. Ryaed will demonstrate how the values of the Riemann zeta function are connected to the mathematics of pi. Ryaed will show how the values of the zeta function, rather than being only the result of the convergence of the zeta function, also have a function regarding the mathematics of circles and are connected to other values of the zeta function via pi. His study also examines how the values of the zeta function are connected to the mathematics of the golden ratio, via the Rogers-Ramanujan continued fraction, which features the golden ratio and the square root of 5.Furthermore, Ryaed Owens has found a method of finding the distribution of prime numbers to infinity, without trial-and-error, which is in turn connected to Euler's product formula, which is connected to the Riemann zeta function. Based on this connection between the mathematics of pi and the zeta function, an argument is put forward on the possibility of the Riemann hypothesis being true.
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.