[PDF] The Development Of Prime Number Theory - eBooks Review

The Development Of Prime Number Theory


The Development Of Prime Number Theory
DOWNLOAD

Download The Development Of Prime Number Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Development Of Prime Number Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page



The Development Of Prime Number Theory


The Development Of Prime Number Theory
DOWNLOAD
Author : Wladyslaw Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14

The Development Of Prime Number Theory written by Wladyslaw Narkiewicz 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 2013-03-14 with Mathematics categories.


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


Number Theory
DOWNLOAD
Author : Benjamin Fine
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-04

Number Theory written by Benjamin Fine 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 2007-06-04 with Mathematics categories.


This book provides an introduction and overview of number theory based on the distribution and properties of primes. This unique approach provides both a firm background in the standard material as well as an overview of the whole discipline. All the essential topics are covered: fundamental theorem of arithmetic, theory of congruences, quadratic reciprocity, arithmetic functions, and the distribution of primes. Analytic number theory and algebraic number theory both receive a solid introductory treatment. The book’s user-friendly style, historical context, and wide range of exercises make it ideal for self study and classroom use.



Multiplicative Number Theory I


Multiplicative Number Theory I
DOWNLOAD
Author : Hugh L. Montgomery
language : en
Publisher: Cambridge University Press
Release Date : 2007

Multiplicative Number Theory I written by Hugh L. Montgomery 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 2007 with Mathematics categories.


A 2006 text based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State.



Prime Numbers


Prime Numbers
DOWNLOAD
Author : Richard Crandall
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-07

Prime Numbers written by Richard Crandall 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 2006-04-07 with Mathematics categories.


Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field



Biscuits Of Number Theory


Biscuits Of Number Theory
DOWNLOAD
Author : Arthur T. Benjamin
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-07-29

Biscuits Of Number Theory written by Arthur T. Benjamin 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 2020-07-29 with Mathematics categories.


An anthology of articles designed to supplement a first course in number theory.



Rational Number Theory In The 20th Century


Rational Number Theory In The 20th Century
DOWNLOAD
Author : Władysław Narkiewicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-02

Rational Number Theory In The 20th Century written by Władysław Narkiewicz 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 2011-09-02 with Mathematics categories.


The last one hundred years have seen many important achievements in the classical part of number theory. After the proof of the Prime Number Theorem in 1896, a quick development of analytical tools led to the invention of various new methods, like Brun's sieve method and the circle method of Hardy, Littlewood and Ramanujan; developments in topics such as prime and additive number theory, and the solution of Fermat’s problem. Rational Number Theory in the 20th Century: From PNT to FLT offers a short survey of 20th century developments in classical number theory, documenting between the proof of the Prime Number Theorem and the proof of Fermat's Last Theorem. The focus lays upon the part of number theory that deals with properties of integers and rational numbers. Chapters are divided into five time periods, which are then further divided into subject areas. With the introduction of each new topic, developments are followed through to the present day. This book will appeal to graduate researchers and student in number theory, however the presentation of main results without technicalities will make this accessible to anyone with an interest in the area.



Number Theoretic Algorithms


Number Theoretic Algorithms
DOWNLOAD
Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :

Number Theoretic Algorithms written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.


"Number Theoretic Algorithms" presents a comprehensive exploration of algorithms specifically designed for number theory applications. Through clear explanations and illustrative examples, this book delves into various algorithmic techniques used to solve fundamental number theoretic problems. From prime number generation to factorization methods, and from modular arithmetic to advanced cryptographic protocols, readers will gain a deep understanding of the algorithms that underpin many important mathematical and cryptographic systems. This invaluable resource equips readers with the tools and insights needed to tackle a wide range of number theoretic challenges.



Analytic Number Theory


Analytic Number Theory
DOWNLOAD
Author : Jean-Marie De Koninck
language : en
Publisher: American Mathematical Society
Release Date : 2023-07-31

Analytic Number Theory written by Jean-Marie De Koninck and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.


The authors assemble a fascinating collection of topics from analytic number theory that provides an introduction to the subject with a very clear and unique focus on the anatomy of integers, that is, on the study of the multiplicative structure of the integers. Some of the most important topics presented are the global and local behavior of arithmetic functions, an extensive study of smooth numbers, the Hardy-Ramanujan and Landau theorems, characters and the Dirichlet theorem, the $abc$ conjecture along with some of its applications, and sieve methods. The book concludes with a whole chapter on the index of composition of an integer. One of this book's best features is the collection of problems at the end of each chapter that have been chosen carefully to reinforce the material. The authors include solutions to the even-numbered problems, making this volume very appropriate for readers who want to test their understanding of the theory presented in the book.



Quadratic Number Theory


Quadratic Number Theory
DOWNLOAD
Author : J. L. Lehman
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-02-13

Quadratic Number Theory written by J. L. Lehman 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 2019-02-13 with Mathematics categories.


Quadratic Number Theory is an introduction to algebraic number theory for readers with a moderate knowledge of elementary number theory and some familiarity with the terminology of abstract algebra. By restricting attention to questions about squares the author achieves the dual goals of making the presentation accessible to undergraduates and reflecting the historical roots of the subject. The representation of integers by quadratic forms is emphasized throughout the text. Lehman introduces an innovative notation for ideals of a quadratic domain that greatly facilitates computation and he uses this to particular effect. The text has an unusual focus on actual computation. This focus, and this notation, serve the author's historical purpose as well; ideals can be seen as number-like objects, as Kummer and Dedekind conceived of them. The notation can be adapted to quadratic forms and provides insight into the connection between quadratic forms and ideals. The computation of class groups and continued fraction representations are featured—the author's notation makes these computations particularly illuminating. Quadratic Number Theory, with its exceptionally clear prose, hundreds of exercises, and historical motivation, would make an excellent textbook for a second undergraduate course in number theory. The clarity of the exposition would also make it a terrific choice for independent reading. It will be exceptionally useful as a fruitful launching pad for undergraduate research projects in algebraic number theory.



Number Theory With Computations


Number Theory With Computations
DOWNLOAD
Author : Peter Shiu
language : en
Publisher: Springer Nature
Release Date : 2024-09-02

Number Theory With Computations written by Peter Shiu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-02 with Mathematics categories.


This introductory text is designed for undergraduate courses in number theory, covering both elementary number theory and analytic number theory. The book emphasises computational aspects, including algorithms and their implementation in Python. The book is divided into two parts. The first part, on elementary number theory, deals with concepts such as induction, divisibility, congruences, primitive roots, cryptography, and continued fractions. The second part is devoted to analytic number theory and includes chapters on Dirichlet’s theorem on primes in arithmetic progressions, the prime number theorem, smooth numbers, and the famous circle method of Hardy and Littlewood. The book contains many topics not often found in introductory textbooks, such as Aubry’s theorem, the Tonelli–Shanks algorithm, factorisation methods, continued fraction representations of e, and the irrationality of ζ(3). Each chapter concludes with a summary and notes, as well as numerous exercises. Assuming only basic calculus for the first part of the book, the second part assumes some knowledge of complex analysis. Familiarity with basic coding syntax will be helpful for the computational exercises.