Introduction to $p$-adic Analytic Number Theory

Introduction to $p$-adic Analytic Number Theory
Author: M. Ram Murty
Publisher: American Mathematical Soc.
Total Pages: 162
Release: 2009-02-09
Genre: Mathematics
ISBN: 0821847740

Download Introduction to $p$-adic Analytic Number Theory Book in PDF, Epub and Kindle

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
Language: en
Pages: 162
Authors: M. Ram Murty
Categories: Mathematics
Type: BOOK - Published: 2009-02-09 - Publisher: American Mathematical Soc.

GET EBOOK

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-expe
Introduction to $p$-adic Analytic Number Theory
Language: en
Pages: 149
Authors: Maruti Ram Murty
Categories: Number theory
Type: BOOK - Published: 2002 - Publisher:

GET EBOOK

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
p-adic Numbers
Language: en
Pages: 285
Authors: Fernando Q. Gouvea
Categories: Mathematics
Type: BOOK - Published: 2013-06-29 - Publisher: Springer Science & Business Media

GET EBOOK

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 num
p-adic Numbers
Language: en
Pages: 366
Authors: Fernando Q. GouvĂȘa
Categories: Mathematics
Type: BOOK - Published: 2020-06-19 - Publisher: Springer Nature

GET EBOOK

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 num
A Course in p-adic Analysis
Language: en
Pages: 451
Authors: Alain M. Robert
Categories: Mathematics
Type: BOOK - Published: 2013-04-17 - Publisher: Springer Science & Business Media

GET EBOOK

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 b