The Distribution of Prime Numbers, Dimitris Koukoulopoulos

Автор: Dimitris Koukoulopoulos
Название: The Distribution of Prime Numbers
ISBN: 1470447541 ISBN-13(EAN): 9781470447540
Издательство: Mare Nostrum (Eurospan)
Цена: 0 T
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Описание: 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.

Автор: Hardy, G. H. (formerly Of The University Of Cambridge) Wright, E. M. (formerly Of The University Of Aberdeen)
Название: Introduction to the theory of numbers
ISBN: 0199219869 ISBN-13(EAN): 9780199219865
Издательство: Oxford Academ
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Цена: 44340.00 T
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Описание: The sixth edition of the classic undergraduate text in elementary number theory includes a new chapter on elliptic curves and their role in the proof of Fermat`s Last Theorem, a foreword by Andrew Wiles and extensively revised and updated end-of-chapter notes.

Автор: Fernando Q Gouv?a
Название: p-adic Numbers: An Introduction
ISBN: 3030472949 ISBN-13(EAN): 9783030472948
Издательство: Springer
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Цена: 51230.00 T
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Описание: There are numbers of all kinds: rational, real, complex, p-adic. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is."

Автор: Dimitris Koukoulopoulos
Название: The Distribution of Prime Numbers
ISBN: 1470447541 ISBN-13(EAN): 9781470447540
Издательство: Mare Nostrum (Eurospan)
Рейтинг:
Цена: 0.00 T
Наличие на складе: Невозможна поставка.
Описание: 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.

Автор: Higgins Peter M.
Название: Numbers: A Very Short Introduction
ISBN: 0199584052 ISBN-13(EAN): 9780199584055
Издательство: Oxford Education
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Цена: 10550.00 T
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Описание: In this Very Short Introduction Peter M. Higgins presents an overview of the number types featured in modern science and mathematics. Providing a non-technical account, he explores the evolution of the modern number system, examines the fascinating role of primes, and explains their role in contemporary cryptography.

Автор: Naji Arwashan
Название: The Riemann Hypothesis and the Distribution of Prime Numbers
ISBN: 1536194220 ISBN-13(EAN): 9781536194227
Издательство: Nova Science
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Цена: 149940.00 T
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Описание: 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. Chapter 1 begins by defining the zeta function and exploring some of its properties when the argument is a real number. It proceeds to identify the series domain of convergence and proves Eulers product formula. Chapter 2 introduces complex numbers and the complex analytic tools necessary to understand the zeta function in complex plane. Chapter 3 extends the domain of the zeta function for the first time by introducing the eta function. Presenting proofs by Sondow, it is shown that zeta can be defined for any complex number whose real part is positive. Next, the functional equation of the zeta function is derived in Chapter 4. This provides a method to extend the definition of zeta to the entirety of the complex plane. Chapter 5 is where the Riemann Hypothesis is properly introduced for the first time. It relates the zeros of the zeta and eta functions which leads to a simple formulation of the hypothesis. Chapters 6 and 7 connect the topics of zetas zeros and the distribution of prime numbers. Chapter 6 introduces Riemann explicit formula and explains the use of Mobius transform to rewrite the prime counting function in terms of the Riemann prime counting one and it provides a detailed numerical example on how to use the Riemanns formula. Chapter 7 derives the von Mangoldt formula via the residue theorem and elucidates some of its important properties. Certain necessary mathematical tools, such as Fourier analysis and theta and gamma functional equations, are included in the appendices to make the chapters more concise and focused.

Автор: Pintz
Название: Irregularities in the Distribution of Prime Numbers
ISBN: 3319927760 ISBN-13(EAN): 9783319927763
Издательство: Springer
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Цена: 60550.00 T
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Описание: This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.

Автор: J?nos Pintz; Michael Th. Rassias
Название: Irregularities in the Distribution of Prime Numbers
ISBN: 3030065146 ISBN-13(EAN): 9783030065140
Издательство: Springer
Рейтинг:
Цена: 60550.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This volume presents research and expository papers highlighting the vibrant and fascinating study of irregularities in the distribution of primes. Written by an international group of experts, contributions present a self-contained yet unified exploration of a rapidly progressing area. Emphasis is given to the research inspired by Maier’s matrix method, which established a newfound understanding of the distribution of primes. Additionally, the book provides an historical overview of a large body of research in analytic number theory and approximation theory. The papers published within are intended as reference tools for graduate students and researchers in mathematics.

Автор: Richard Crandall; Carl B. Pomerance
Название: Prime Numbers
ISBN: 1441920501 ISBN-13(EAN): 9781441920508
Издательство: Springer
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Цена: 102480.00 T
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Описание: Bridges the gap between theoretical and computational aspects of prime numbersExercise sections are a goldmine of interesting examples, pointers to the literature and potential research projectsAuthors are well-known and highly-regarded in the field

Автор: Hilley Joe
Название: Observations Regarding Non-Prime Odd Numbers
ISBN: 1736410512 ISBN-13(EAN): 9781736410516
Издательство: Неизвестно
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Цена: 16630.00 T
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Описание:

For centuries, mathematicians have been captivated by the mystery of prime numbers. Their effort to decipher that mystery has focused on the most abstract mathematics concepts and techniques known. Yet still they have no answers. Others, frustrated by the nature of earlier attempts, have suggested the primes can be counted by a much simpler method using calculations that involve the numbers that are not prime-identifying and removing them until only prime numbers remain.

In Observations Regarding Non-Prime Odd Numbers, New York Times bestselling author Joe Hilley examines non-prime numbers in an attempt to gain clues about the nature of prime numbers, their propagation, and occurrence. Informative, readable, and entertaining, Joe provides clues you won't find anywhere else and surprising insights sure to generate lively debate.

Автор: Ribenboim Paulo
Название: Prime Numbers, Friends Who Give Problems: A Trialogue With Papa Paulo
ISBN: 9814725803 ISBN-13(EAN): 9789814725804
Издательство: World Scientific Publishing
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Цена: 65470.00 T
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Описание:

"This is a charming book, written as a conversation between mathematician Papa Paulo and his grandsons. A motivated reader can learn not only about prime numbers, but also something about how mathematicians think, work, and ask questions from reading this book."

Mathematical Association of America

Prime Numbers, Friends Who Give Problems is written as a trialogue, with two persons who are interested in prime numbers asking the author, Papa Paulo, intelligent questions. Starting at a very elementary level, the book advances steadily, covering all important topics of the theory of prime numbers, up to the most famous problems. The humorous conversations and the inclusion of a back-story add to the uniqueness of the book. Concepts and results are also explained with great care, making the book accessible to a wide audience.

Автор: Escassut Alain
Название: Value Distribution In P-Adic Analysis
ISBN: 9814730106 ISBN-13(EAN): 9789814730105
Издательство: World Scientific Publishing
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Цена: 190080.00 T
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The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.

Автор: Paul Alan Vojta
Название: Diophantine Approximations and Value Distribution Theory
ISBN: 3540175512 ISBN-13(EAN): 9783540175513
Издательство: Springer
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Цена: 23250.00 T
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