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Introduction to $p$-adic Analytic Number Theory

2009-02-09 Mathematics
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Release : 2009-02-09
Genre : Mathematics
Kind : eBook
Book Rating : 740/5 ( reviews)

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Book Synopsis Introduction to $p$-adic Analytic Number Theory by : M. Ram Murty

Download or read book Introduction to $p$-adic Analytic Number Theory written by M. Ram Murty. This book was released on 2009-02-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to $p$-adic Analytic Number Theory

2002 Number theory
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Release : 2002
Genre : Number theory
Kind : eBook
Book Rating : 420/5 ( reviews)

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Book Synopsis Introduction to $p$-adic Analytic Number Theory by : Maruti Ram Murty

Download or read book Introduction to $p$-adic Analytic Number Theory written by Maruti Ram Murty. This book was released on 2002. Available in PDF, EPUB and Kindle. Book excerpt: 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.

p-adic Numbers

2013-06-29 Mathematics
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Release : 2013-06-29
Genre : Mathematics
Kind : eBook
Book Rating : 787/5 ( reviews)

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Book Synopsis p-adic Numbers by : Fernando Q. Gouvea

Download or read book p-adic Numbers written by Fernando Q. Gouvea. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: 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

2020-06-19 Mathematics
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Release : 2020-06-19
Genre : Mathematics
Kind : eBook
Book Rating : 957/5 ( reviews)

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Book Synopsis p-adic Numbers by : Fernando Q. Gouvêa

Download or read book p-adic Numbers written by Fernando Q. Gouvêa. This book was released on 2020-06-19. Available in PDF, EPUB and Kindle. Book excerpt: 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

P-adic Analysis and Mathematical Physics

1994 Science
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Release : 1994
Genre : Science
Kind : eBook
Book Rating : 806/5 ( reviews)

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Book Synopsis P-adic Analysis and Mathematical Physics by : Vasili? Sergeevich Vladimirov

Download or read book P-adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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