P Adic Numbers

Author : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 55,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662222782

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p-adic Numbers by Fernando Q. Gouvea Pdf

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.

Author : Fernando Gouvea
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 44,7 Mb
Release : 2003-05-22
Category : Mathematics
ISBN : 3540629114

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p-adic Numbers by Fernando Gouvea Pdf

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

Author : Alain M. Robert
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 46,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475732542

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A Course in p-adic Analysis by Alain M. Robert Pdf

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.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211129

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p-adic Numbers, p-adic Analysis, and Zeta-Functions by Neal Koblitz Pdf

The first edition of this work has become the standard introduction to the theory of p-adic numbers at both the advanced undergraduate and beginning graduate level. This second edition includes a deeper treatment of p-adic functions in Ch. 4 to include the Iwasawa logarithm and the p-adic gamma-function, the rearrangement and addition of some exercises, the inclusion of an extensive appendix of answers and hints to the exercises, as well as numerous clarifications.

Author : Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov
Publisher : World Scientific
Page : 350 pages
File Size : 46,5 Mb
Release : 1994
Category : Science
ISBN : 9810208804

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P-adic Analysis and Mathematical Physics by Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov Pdf

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.

Author : Svetlana Katok
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 49,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842201

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P-adic Analysis Compared with Real by Svetlana Katok Pdf

The book gives an introduction to $p$-adic numbers from the point of view of number theory, topology, and analysis. Compared to other books on the subject, its novelty is both a particularly balanced approach to these three points of view and an emphasis on topics accessible to undergraduates. In addition, several topics from real analysis and elementary topology which are not usually covered in undergraduate courses (totally disconnected spaces and Cantor sets, points of discontinuity of maps and the Baire Category Theorem, surjectivity of isometries of compact metric spaces) are also included in the book. They will enhance the reader's understanding of real analysis and intertwine the real and $p$-adic contexts of the book. The book is based on an advanced undergraduate course given by the author. The choice of the topic was motivated by the internal beauty of the subject of $p$-adic analysis, an unusual one in the undergraduate curriculum, and abundant opportunities to compare it with its much more familiar real counterpart. The book includes a large number of exercises. Answers, hints, and solutions for most of them appear at the end of the book. Well written, with obvious care for the reader, the book can be successfully used in a topic course or for self-study.

Author : M. Ram Murty
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 43,5 Mb
Release : 2009-02-09
Category : Mathematics
ISBN : 9780821847749

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Introduction to $p$-adic Analytic Number Theory by M. Ram Murty Pdf

This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.

Author : Andrei Y. Khrennikov
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401583565

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p-Adic Valued Distributions in Mathematical Physics by Andrei Y. Khrennikov Pdf

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

Author : Fernando Q. Gouvea
Publisher : Springer
Page : 129 pages
File Size : 45,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540388548

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Arithmetic of p-adic Modular Forms by Fernando Q. Gouvea Pdf

The central topic of this research monograph is the relation between p-adic modular forms and p-adic Galois representations, and in particular the theory of deformations of Galois representations recently introduced by Mazur. The classical theory of modular forms is assumed known to the reader, but the p-adic theory is reviewed in detail, with ample intuitive and heuristic discussion, so that the book will serve as a convenient point of entry to research in that area. The results on the U operator and on Galois representations are new, and will be of interest even to the experts. A list of further problems in the field is included to guide the beginner in his research. The book will thus be of interest to number theorists who wish to learn about p-adic modular forms, leading them rapidly to interesting research, and also to the specialists in the subject.

Author : Heinz-Dieter Ebbinghaus
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 42,8 Mb
Release : 1991
Category : Mathematics
ISBN : 0387974970

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Numbers by Heinz-Dieter Ebbinghaus Pdf

This book is about all kinds of numbers, from rationals to octonians, reals to infinitesimals. It is a story about a major thread of mathematics over thousands of years, and it answers everything from why Hamilton was obsessed with quaternions to what the prospect was for quaternionic analysis in the 19th century. It glimpses the mystery surrounding imaginary numbers in the 17th century and views some major developments of the 20th century.

Author : Kurt Mahler
Publisher : CUP Archive
Page : 114 pages
File Size : 46,9 Mb
Release : 1973-03-29
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to P-Adic Numbers and Their Functions by Kurt Mahler Pdf

Author : Andrei Y. Khrennikov,Marcus Nilsson
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 42,5 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781402026607

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P-adic Deterministic and Random Dynamics by Andrei Y. Khrennikov,Marcus Nilsson Pdf

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.

Author : George Bachman
Publisher : Unknown
Page : 196 pages
File Size : 52,7 Mb
Release : 1964
Category : Algebraic fields
ISBN : UOM:39015065682224

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Introduction to P-adic Numbers and Valuation Theory by George Bachman Pdf

Author : William P. Berlinghoff,Fernando Q. Gouvêa
Publisher : American Mathematical Soc.
Page : 331 pages
File Size : 41,5 Mb
Release : 2021-04-29
Category : Education
ISBN : 9781470464561

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Math through the Ages: A Gentle History for Teachers and Others Expanded Second Edition by William P. Berlinghoff,Fernando Q. Gouvêa Pdf

Where did math come from? Who thought up all those algebra symbols, and why? What is the story behind π π? … negative numbers? … the metric system? … quadratic equations? … sine and cosine? … logs? The 30 independent historical sketches in Math through the Ages answer these questions and many others in an informal, easygoing style that is accessible to teachers, students, and anyone who is curious about the history of mathematical ideas. Each sketch includes Questions and Projects to help you learn more about its topic and to see how the main ideas fit into the bigger picture of history. The 30 short stories are preceded by a 58-page bird's-eye overview of the entire panorama of mathematical history, a whirlwind tour of the most important people, events, and trends that shaped the mathematics we know today. “What to Read Next” and reading suggestions after each sketch provide starting points for readers who want to learn more. This book is ideal for a broad spectrum of audiences, including students in history of mathematics courses at the late high school or early college level, pre-service and in-service teachers, and anyone who just wants to know a little more about the origins of mathematics.

Author : Kiran S. Kedlaya
Publisher : Cambridge University Press
Page : 399 pages
File Size : 41,6 Mb
Release : 2010-06-10
Category : Mathematics
ISBN : 9781139489201

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p-adic Differential Equations by Kiran S. Kedlaya Pdf

Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.