Introduction To P Adic Analytic Number Theory

Author : M. Ram Murty
Publisher : American Mathematical Soc.
Page : 149 pages
File Size : 43,9 Mb
Release : 2009-02-09
Category : Number theory
ISBN : 9780821847749

Get Book

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 : Maruti Ram Murty
Publisher : Unknown
Page : 149 pages
File Size : 53,6 Mb
Release : 2002
Category : Number theory
ISBN : 1470417421

Get Book

Introduction to $p$-adic Analytic Number Theory by Maruti 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-functi.

Author : A. G. Postnikov
Publisher : American Mathematical Soc.
Page : 332 pages
File Size : 49,7 Mb
Release : 1988-12-31
Category : Mathematics
ISBN : 9780821813492

Get Book

Introduction to Analytic Number Theory by A. G. Postnikov Pdf

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 : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 51,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662222782

Get Book

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 : U.S.R. Murty
Publisher : Springer Science & Business Media
Page : 458 pages
File Size : 41,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475734416

Get Book

Problems in Analytic Number Theory by U.S.R. Murty Pdf

"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 : Bateman Paul Trevier,Diamond Harold G
Publisher : World Scientific
Page : 376 pages
File Size : 47,5 Mb
Release : 2004-09-07
Category : Mathematics
ISBN : 9789814365567

Get Book

Analytic Number Theory: An Introductory Course by Bateman Paul Trevier,Diamond Harold G Pdf

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 www.math.uiuc.edu/~diamond/.

Author : Vasili? Sergeevich Vladimirov,I. V. Volovich,E. I. Zelenov
Publisher : World Scientific
Page : 350 pages
File Size : 45,6 Mb
Release : 1994
Category : Science
ISBN : 9810208804

Get Book

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 : 49,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842201

Get Book

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 : Kurt Mahler
Publisher : CUP Archive
Page : 114 pages
File Size : 55,9 Mb
Release : 1973-03-29
Category : Mathematics
ISBN : 8210379456XXX

Get Book

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

Author : Komaravolu Chandrasekharan
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642461248

Get Book

Introduction to Analytic Number Theory by Komaravolu Chandrasekharan Pdf

This book has grown out of a course of lectures I have given at the Eidgenossische Technische Hochschule, Zurich. Notes of those lectures, prepared for the most part by assistants, have appeared in German. This book follows the same general plan as those notes, though in style, and in text (for instance, Chapters III, V, VIII), and in attention to detail, it is rather different. Its purpose is to introduce the non-specialist to some of the fundamental results in the theory of numbers, to show how analytical methods of proof fit into the theory, and to prepare the ground for a subsequent inquiry into deeper questions. It is pub lished in this series because of the interest evinced by Professor Beno Eckmann. I have to acknowledge my indebtedness to Professor Carl Ludwig Siegel, who has read the book, both in manuscript and in print, and made a number of valuable criticisms and suggestions. Professor Raghavan Narasimhan has helped me, time and again, with illuminating comments. Dr. Harold Diamond has read the proofs, and helped me to remove obscurities. I have to thank them all. K.C.

Author : Neal Koblitz
Publisher : Cambridge University Press
Page : 171 pages
File Size : 42,9 Mb
Release : 1980-11-28
Category : Mathematics
ISBN : 9780521280600

Get Book

P-adic Analysis by Neal Koblitz Pdf

An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
Page : 163 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461211129

Get Book

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 : Tom M. Apostol
Publisher : Springer Science & Business Media
Page : 352 pages
File Size : 50,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475755794

Get Book

Introduction to Analytic Number Theory by Tom M. Apostol Pdf

"This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages."-—MATHEMATICAL REVIEWS

Author : Anatolij A. Karatsuba
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 42,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580185

Get Book

Basic Analytic Number Theory by Anatolij A. Karatsuba Pdf

This English translation of Karatsuba's Basic Analytic Number Theory follows closely the second Russian edition, published in Moscow in 1983. For the English edition, the author has considerably rewritten Chapter I, and has corrected various typographical and other minor errors throughout the the text. August, 1991 Melvyn B. Nathanson Introduction to the English Edition It gives me great pleasure that Springer-Verlag is publishing an English trans lation of my book. In the Soviet Union, the primary purpose of this monograph was to introduce mathematicians to the basic results and methods of analytic number theory, but the book has also been increasingly used as a textbook by graduate students in many different fields of mathematics. I hope that the English edition will be used in the same ways. I express my deep gratitude to Professor Melvyn B. Nathanson for his excellent translation and for much assistance in correcting errors in the original text. A.A. Karatsuba Introduction to the Second Russian Edition Number theory is the study of the properties of the integers. Analytic number theory is that part of number theory in which, besides purely number theoretic arguments, the methods of mathematical analysis play an essential role.

Author : Alain M. Robert
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 46,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475732542

Get Book

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.