Irregularities In The Distribution Of Prime Numbers

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Irregularities in the Distribution of Prime Numbers

Author : János Pintz
Publisher : Springer
ISBN 13 : 3319927779
Total Pages : 217 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Irregularities in the Distribution of Prime Numbers by : János Pintz

Download or read book Irregularities in the Distribution of Prime Numbers written by János Pintz and published by Springer. This book was released on 2018-07-04 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Distribution of Prime Numbers

Author : Dimitris Koukoulopoulos
Publisher : American Mathematical Soc.
ISBN 13 : 1470462850
Total Pages : 356 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Distribution of Prime Numbers by : Dimitris Koukoulopoulos

Download or read book The Distribution of Prime Numbers written by Dimitris Koukoulopoulos and published by American Mathematical Soc.. This book was released on 2020-07-28 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Distribution of Prime Numbers

Author : Albert Edward Ingham
Publisher : Cambridge University Press
ISBN 13 : 9780521397896
Total Pages : 140 pages
Book Rating : 4.3/5 (978 download)

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Book Synopsis The Distribution of Prime Numbers by : Albert Edward Ingham

Download or read book The Distribution of Prime Numbers written by Albert Edward Ingham and published by Cambridge University Press. This book was released on 1990-09-28 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Distribution of Prime Numbers

Author : Osric Allen
Publisher : Robert Temple Books
ISBN 13 : 9780952309369
Total Pages : 20 pages
Book Rating : 4.3/5 (93 download)

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Book Synopsis The Distribution of Prime Numbers by : Osric Allen

Download or read book The Distribution of Prime Numbers written by Osric Allen and published by Robert Temple Books. This book was released on 2006 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Unsolved Problems in Number Theory

Author : Richard Guy
Publisher : Springer Science & Business Media
ISBN 13 : 0387266771
Total Pages : 455 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Unsolved Problems in Number Theory by : Richard Guy

Download or read book Unsolved Problems in Number Theory written by Richard Guy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.

Equidistribution in Number Theory, An Introduction

Author : Andrew Granville
Publisher : Springer Science & Business Media
ISBN 13 : 1402054041
Total Pages : 356 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Equidistribution in Number Theory, An Introduction by : Andrew Granville

Download or read book Equidistribution in Number Theory, An Introduction written by Andrew Granville and published by Springer Science & Business Media. This book was released on 2007-04-08 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. The volume brings together leading researchers from a range of fields who reveal fascinating links between seemingly disparate areas.

Solved and Unsolved Problems in Number Theory

Author : Daniel Shanks
Publisher : American Mathematical Society
ISBN 13 : 1470476452
Total Pages : 321 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Solved and Unsolved Problems in Number Theory by : Daniel Shanks

Download or read book Solved and Unsolved Problems in Number Theory written by Daniel Shanks and published by American Mathematical Society. This book was released on 2024-01-24 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The investigation of three problems, perfect numbers, periodic decimals, and Pythagorean numbers, has given rise to much of elementary number theory. In this book, Daniel Shanks, past editor of Mathematics of Computation, shows how each result leads to further results and conjectures. The outcome is a most exciting and unusual treatment. This edition contains a new chapter presenting research done between 1962 and 1978, emphasizing results that were achieved with the help of computers.

European Congress of Mathematics

Author : Antal Balog
Publisher : Springer Science & Business Media
ISBN 13 : 9783764354978
Total Pages : 364 pages
Book Rating : 4.3/5 (549 download)

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Book Synopsis European Congress of Mathematics by : Antal Balog

Download or read book European Congress of Mathematics written by Antal Balog and published by Springer Science & Business Media. This book was released on 1998-07-21 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua

Proceedings of the International Congress of Mathematicians

Author : S.D. Chatterji
Publisher : Birkhäuser
ISBN 13 : 3034890788
Total Pages : 1669 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Proceedings of the International Congress of Mathematicians by : S.D. Chatterji

Download or read book Proceedings of the International Congress of Mathematicians written by S.D. Chatterji and published by Birkhäuser. This book was released on 2012-12-06 with total page 1669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)

The New Book of Prime Number Records

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
ISBN 13 : 1461207592
Total Pages : 558 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The New Book of Prime Number Records by : Paulo Ribenboim

Download or read book The New Book of Prime Number Records written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium senes. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book of Records, reminded me very gently that the most "innumerate" people of the world are of a certain trible in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes, Morris, I'm from Brazil, but my book will contain numbers different from ·one.''' He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name) and consists of about 16 million decimal digits of the number Te. "I assure you, Morris, that in spite of the beauty of the appar ent randomness of the decimal digits of Te, I'll be sure that my text will include also some words." And then I proceeded putting together the magic combina tion of words and numbers, which became The Book of Prime Number Records. If you have seen it, only extreme curiosity could impel you to have this one in your hands. The New Book of Prime Number Records differs little from its predecessor in the general planning. But it contains new sections and updated records.

The Book of Prime Number Records

Author : Paulo Ribenboim
Publisher : Springer Science & Business Media
ISBN 13 : 1468499386
Total Pages : 492 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis The Book of Prime Number Records by : Paulo Ribenboim

Download or read book The Book of Prime Number Records written by Paulo Ribenboim and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text originated as a lecture delivered November 20, 1984, at Queen's University, in the undergraduate colloquium series established to honour Professors A. J. Coleman and H. W. Ellis and to acknowledge their long-lasting interest in the quality of teaching undergraduate students. In another colloquium lecture, my colleague Morris Orzech, who had consulted the latest edition of the Guinness Book oj Records, reminded me very gently that the most "innumerate" people of the world are of a certain tribe in Mato Grosso, Brazil. They do not even have a word to express the number "two" or the concept of plurality. "Yes Morris, I'm from Brazil, but my book will contain numbers different from 'one.' " He added that the most boring 800-page book is by two Japanese mathematicians (whom I'll not name), and consists of about 16 million digits of the number 11. "I assure you Morris, that in spite of the beauty of the apparent randomness of the decimal digits of 11, I'll be sure that my text will also include some words." Acknowledgment. The manuscript of this book was prepared on the word processor by Linda Nuttall. I wish to express my appreciation for the great care, speed, and competence of her work. Paulo Ribenboim CONTENTS Preface vii Guiding the Reader xiii Index of Notations xv Introduction Chapter 1. How Many Prime Numbers Are There? 3 I. Euclid's Proof 3 II.

The Development of Prime Number Theory

Author : Wladyslaw Narkiewicz
Publisher : Springer Science & Business Media
ISBN 13 : 3662131579
Total Pages : 457 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis The Development of Prime Number Theory by : Wladyslaw Narkiewicz

Download or read book The Development of Prime Number Theory written by Wladyslaw Narkiewicz and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. People were already interested in prime numbers in ancient times, and the first result concerning the distribution of primes appears in Euclid's Elemen ta, where we find a proof of their infinitude, now regarded as canonical. One feels that Euclid's argument has its place in The Book, often quoted by the late Paul ErdOs, where the ultimate forms of mathematical arguments are preserved. Proofs of most other results on prime number distribution seem to be still far away from their optimal form and the aim of this book is to present the development of methods with which such problems were attacked in the course of time. This is not a historical book since we refrain from giving biographical details of the people who have played a role in this development and we do not discuss the questions concerning why each particular person became in terested in primes, because, usually, exact answers to them are impossible to obtain. Our idea is to present the development of the theory of the distribu tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century. We shall also present some later developments, mostly in short comments, although the reader will find certain exceptions to that rule. The period of the last 80 years was full of new ideas (we mention only the applications of trigonometrical sums or the advent of various sieve methods) and certainly demands a separate book.

Number Theory and Symmetry

Author : Michel Planat
Publisher : MDPI
ISBN 13 : 3039366866
Total Pages : 206 pages
Book Rating : 4.0/5 (393 download)

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Book Synopsis Number Theory and Symmetry by : Michel Planat

Download or read book Number Theory and Symmetry written by Michel Planat and published by MDPI. This book was released on 2021-01-20 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.

The Life of Primes in 37 Episodes

Author : Jean-Marie De Koninck
Publisher : American Mathematical Soc.
ISBN 13 : 1470464896
Total Pages : 329 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Life of Primes in 37 Episodes by : Jean-Marie De Koninck

Download or read book The Life of Primes in 37 Episodes written by Jean-Marie De Koninck and published by American Mathematical Soc.. This book was released on 2021-05-19 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the life of primes. Indeed, once they are defined, primes take on a life of their own and the mysteries surrounding them begin multiplying, just like living cells reproduce themselves, and there seems to be no end to it. This monograph takes the reader on a journey through time, providing an accessible overview of the numerous prime number theory problems that mathematicians have been working on since Euclid. Topics are presented in chronological order as episodes. These include results on the distribution of primes, from the most elementary to the proof of the famous prime number theorem. The book also covers various primality tests and factorisation algorithms. It is then shown how our inability to factor large integers has allowed mathematicians to create today's most secure encryption method. Computer science buffs may be tempted to tackle some of the many open problems appearing in the episodes. Throughout the presentation, the human side of mathematics is displayed through short biographies that give a glimpse of the lives of the people who contributed to the life of primes. Each of the 37 episodes concludes with a series of problems (many with solutions) that will assist the reader in gaining a better understanding of the theory.

Number Theory

Author : W.A. Coppel
Publisher : Springer Science & Business Media
ISBN 13 : 0387894853
Total Pages : 620 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Number Theory by : W.A. Coppel

Download or read book Number Theory written by W.A. Coppel and published by Springer Science & Business Media. This book was released on 2009-08-12 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Number Theory is more than a comprehensive treatment of the subject. It is an introduction to topics in higher level mathematics, and unique in its scope; topics from analysis, modern algebra, and discrete mathematics are all included. The book is divided into two parts. Part A covers key concepts of number theory and could serve as a first course on the subject. Part B delves into more advanced topics and an exploration of related mathematics. The prerequisites for this self-contained text are elements from linear algebra. Valuable references for the reader are collected at the end of each chapter. It is suitable as an introduction to higher level mathematics for undergraduates, or for self-study.

Mathematical Constants

Author : Steven R. Finch
Publisher : Cambridge University Press
ISBN 13 : 9780521818056
Total Pages : 634 pages
Book Rating : 4.8/5 (18 download)

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Book Synopsis Mathematical Constants by : Steven R. Finch

Download or read book Mathematical Constants written by Steven R. Finch and published by Cambridge University Press. This book was released on 2003-08-18 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steven Finch provides 136 essays, each devoted to a mathematical constant or a class of constants, from the well known to the highly exotic. This book is helpful both to readers seeking information about a specific constant, and to readers who desire a panoramic view of all constants coming from a particular field, for example, combinatorial enumeration or geometric optimization. Unsolved problems appear virtually everywhere as well. This work represents an outstanding scholarly attempt to bring together all significant mathematical constants in one place.

Prime Numbers: The Holy Grail Of Mathematics

Author : Thamer Naouech
Publisher : Thamer Naouech
ISBN 13 :
Total Pages : 46 pages
Book Rating : 4.6/5 (975 download)

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Book Synopsis Prime Numbers: The Holy Grail Of Mathematics by : Thamer Naouech

Download or read book Prime Numbers: The Holy Grail Of Mathematics written by Thamer Naouech and published by Thamer Naouech. This book was released on 2020-10-20 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is undeniable how prime numbers are one of the most beautiful and fascinating topics in mathematics. But what are prime numbers? Are they only numbers that are divisible by 1 and themselves, or do they have another interesting hidden face?Throughout history, the mystery of prime numbers has challenged the greatest minds in mathematics starting from Euclid of Alexandria to Fermat, Euler, Gauss, and Erdős,… who attempted to solve the puzzling problem of primes. The achievements they realized and the secrets they revealed can only assert how deep the concept of prime numbers is. Starting from how prime numbers exist in nature, and how they are of great use in modern cryptography on which our daily life completely depends, the author travels in the holy kingdom of primes diving into some conjectures involving those special numbers. From the Riemann Hypothesis and the well-known zeta function, he explains how a note in the margin turned to be Fermat’s Last Theorem, one of the most important problems in the history of mathematics. From Mersenne Primes, he gets to the twin primes, those shining little stars in the blue sky of primes. And from Euclid’s proof of the infinite number of primes he gets to a hidden pattern in the distribution of primes discovered by Stanisław Ulam and called the Ulam Spiral. After this little trip, you will know, dear reader, why prime numbers deserve to be called "the holy grail of mathematics".