Introduction To P Adic Analytic Number Theory
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Author |
: M. Ram Murty |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 162 |
Release |
: 2009-02-09 |
ISBN-10 |
: 9780821847749 |
ISBN-13 |
: 0821847740 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Introduction to $p$-adic Analytic Number Theory by : M. Ram Murty
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 |
: Maruti Ram Murty |
Publisher |
: |
Total Pages |
: 149 |
Release |
: 2002 |
ISBN-10 |
: 1470417421 |
ISBN-13 |
: 9781470417420 |
Rating |
: 4/5 (21 Downloads) |
Synopsis Introduction to $p$-adic Analytic Number Theory by : Maruti Ram Murty
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-functi.
Author |
: Fernando Q. Gouvêa |
Publisher |
: Springer Nature |
Total Pages |
: 366 |
Release |
: 2020-06-19 |
ISBN-10 |
: 9783030472955 |
ISBN-13 |
: 3030472957 |
Rating |
: 4/5 (55 Downloads) |
Synopsis p-adic Numbers by : Fernando Q. Gouvêa
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 |
: Fernando Q. Gouvea |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 285 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9783662222782 |
ISBN-13 |
: 3662222787 |
Rating |
: 4/5 (82 Downloads) |
Synopsis p-adic Numbers by : Fernando Q. Gouvea
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 |
: A. G. Postnikov |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 332 |
Release |
: 1988-12-31 |
ISBN-10 |
: 9780821813492 |
ISBN-13 |
: 0821813498 |
Rating |
: 4/5 (92 Downloads) |
Synopsis Introduction to Analytic Number Theory by : A. G. Postnikov
Aimed at a level between textbooks and the latest research monographs, this book is directed at researchers, teachers, and graduate students interested in number theory and its connections with other branches of science. Choosing to emphasize topics not sufficiently covered in the literature, the author has attempted to give as broad a picture as possible of the problems of analytic number theory.
Author |
: Alain M. Robert |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 451 |
Release |
: 2013-04-17 |
ISBN-10 |
: 9781475732542 |
ISBN-13 |
: 1475732546 |
Rating |
: 4/5 (42 Downloads) |
Synopsis A Course in p-adic Analysis by : Alain M. Robert
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 |
: Svetlana Katok |
Publisher |
: American Mathematical Soc. |
Total Pages |
: 170 |
Release |
: 2007 |
ISBN-10 |
: 9780821842201 |
ISBN-13 |
: 082184220X |
Rating |
: 4/5 (01 Downloads) |
Synopsis $p$-adic Analysis Compared with Real by : Svetlana Katok
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 |
: Vasili? Sergeevich Vladimirov |
Publisher |
: World Scientific |
Total Pages |
: 350 |
Release |
: 1994 |
ISBN-10 |
: 9810208804 |
ISBN-13 |
: 9789810208806 |
Rating |
: 4/5 (04 Downloads) |
Synopsis P-adic Analysis and Mathematical Physics by : Vasili? Sergeevich Vladimirov
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 |
: U.S.R. Murty |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 458 |
Release |
: 2013-06-29 |
ISBN-10 |
: 9781475734416 |
ISBN-13 |
: 1475734417 |
Rating |
: 4/5 (16 Downloads) |
Synopsis Problems in Analytic Number Theory by : U.S.R. Murty
"In order to become proficient in mathematics, or in any subject," writes Andre Weil, "the student must realize that most topics in volve only a small number of basic ideas. " After learning these basic concepts and theorems, the student should "drill in routine exercises, by which the necessary reflexes in handling such concepts may be ac quired. . . . There can be no real understanding of the basic concepts of a mathematical theory without an ability to use them intelligently and apply them to specific problems. " Weil's insightfulobservation becomes especially important at the graduate and research level. It is the viewpoint of this book. Our goal is to acquaint the student with the methods of analytic number theory as rapidly as possible through examples and exercises. Any landmark theorem opens up a method of attacking other problems. Unless the student is able to sift out from the mass of theory the underlying techniques, his or her understanding will only be academic and not that of a participant in research. The prime number theorem has given rise to the rich Tauberian theory and a general method of Dirichlet series with which one can study the asymptotics of sequences. It has also motivated the development of sieve methods. We focus on this theme in the book. We also touch upon the emerging Selberg theory (in Chapter 8) and p-adic analytic number theory (in Chapter 10).
Author |
: P. T. Bateman |
Publisher |
: World Scientific |
Total Pages |
: 378 |
Release |
: 2004 |
ISBN-10 |
: 9812560807 |
ISBN-13 |
: 9789812560803 |
Rating |
: 4/5 (07 Downloads) |
Synopsis Analytic Number Theory by : P. T. Bateman
This valuable book focuses on a collection of powerful methods of analysis that yield deep number-theoretical estimates. Particular attention is given to counting functions of prime numbers and multiplicative arithmetic functions. Both real variable (?elementary?) and complex variable (?analytic?) methods are employed. The reader is assumed to have knowledge of elementary number theory (abstract algebra will also do) and real and complex analysis. Specialized analytic techniques, including transform and Tauberian methods, are developed as needed.Comments and corrigenda for the book are found at http: //www.math.uiuc.edu/ diamond/