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AMS/IP Studies in Advanced Mathematics

Volume 27

Introduction to p-adic Analytic Number Theory

M. Ram Murty

Textbook

Original Publication: 2002

Publisher: American Mathematical Society / International Press

Language: English

Paperback

149 pages

Description

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.

The book treats the subject informally, making the text accessible to non-experts. It would make a nice independent text for a course geared toward advanced undergraduates through beginning graduate students.

This volume is part of the AMS/IP Studies in Advanced Mathematics book series.

Publications

Pub. Date

ISBN-13

ISBN-10

Medium

Binding

Size, Etc.

Status

List Price

2015 Jan

9780821888308

0821888307

Print

paperback

In Print

2015 Jan

9780821847749

0821847740

Print

paperback

In Print

2002

9780821832622

082183262X

Print

hardcover

In Print

US$43.00