p-adic Numbers

Mathematics
p-adic Numbers PDF Author: Fernando Q. Gouvea
Publisher: Springer Science & Business Media
ISBN: 3662222787
Category : Mathematics
Languages : en
Pages : 282

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Book Description
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

p-adic Numbers

p-adic Numbers PDF Author: Fernando Q. Gouvea
Publisher: Springer Science & Business Media
ISBN: 3662222787
Category : Mathematics
Languages : en
Pages : 282

View

Book Description
p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

p-adic Numbers

p-adic Numbers PDF Author: Fernando Q. GouvĂȘa
Publisher: Springer Nature
ISBN: 3030472957
Category : Mathematics
Languages : en
Pages : 366

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Book Description
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. 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." --THE MATHEMATICAL GAZETTE

Number Theory

Number Theory PDF Author:
Publisher: Academic Press
ISBN: 9780080873329
Category : Mathematics
Languages : en
Pages : 434

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Book Description
This book is written for the student in mathematics. Its goal is to give a view of the theory of numbers, of the problems with which this theory deals, and of the methods that are used. We have avoided that style which gives a systematic development of the apparatus and have used instead a freer style, in which the problems and the methods of solution are closely interwoven. We start from concrete problems in number theory. General theories arise as tools for solving these problems. As a rule, these theories are developed sufficiently far so that the reader can see for himself their strength and beauty, and so that he learns to apply them. Most of the questions that are examined in this book are connected with the theory of diophantine equations - that is, with the theory of the solutions in integers of equations in several variables. However, we also consider questions of other types; for example, we derive the theorem of Dirichlet on prime numbers in arithmetic progressions and investigate the growth of the number of solutions of congruences.

A Course in p-adic Analysis

A Course in p-adic Analysis PDF Author: Alain M. Robert
Publisher: Springer Science & Business Media
ISBN: 9780387986692
Category : Mathematics
Languages : en
Pages : 438

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Book Description
Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.

P-adic Analysis and Mathematical Physics

P-adic Analysis and Mathematical Physics PDF Author: Vasili? Sergeevich Vladimirov
Publisher: World Scientific
ISBN: 9789810208806
Category : Science
Languages : en
Pages : 319

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Book Description
p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.

P-adic Deterministic and Random Dynamics

P-adic Deterministic and Random Dynamics PDF Author: Andrei Y. Khrennikov
Publisher: Springer Science & Business Media
ISBN: 1402026609
Category : Science
Languages : en
Pages : 270

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Book Description
This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.

Arithmetic Differential Operators Over the P-adic Integers

Arithmetic Differential Operators Over the P-adic Integers PDF Author: Claire C. Ralph
Publisher: Cambridge University Press
ISBN: 110767414X
Category : Mathematics
Languages : en
Pages : 139

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Book Description
This complete introduction to the study of arithmetic differential operators over the p-adic integers offers graduate students and researchers an accessible guide to this novel and promising area of mathematics. It starts with the basics and is accessible to anyone with a basic grasp of algebraic number theory.

Introduction to P-Adic Numbers and Their Functions

Introduction to P-Adic Numbers and Their Functions PDF Author: Kurt Mahler
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 91

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Book Description


Number Theory 1

Number Theory 1 PDF Author: Kazuya Kato
Publisher: American Mathematical Soc.
ISBN: 9780821808634
Category : Mathematics
Languages : en
Pages : 154

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Book Description
This is an inexpensive softcover volume that focuses on number theory and plays off of Fermat's Last Theorem, which was solved recently and which is still among the top stories in mathematics. Another excellent book for the bookselling venue.

Theory of P-adic Distributions

Theory of P-adic Distributions PDF Author: S. Albeverio
Publisher: Cambridge University Press
ISBN: 0521148561
Category : Mathematics
Languages : en
Pages : 351

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Book Description
A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.