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p-adic Numbers, p-adic Analysis, and Zeta-Functions

2012-12-06 Mathematics
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Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 123/5 ( reviews)

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Book Synopsis p-adic Numbers, p-adic Analysis, and Zeta-Functions by : Neal Koblitz

Download or read book p-adic Numbers, p-adic Analysis, and Zeta-Functions written by Neal Koblitz. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Course in p-adic Analysis

2013-04-17 Mathematics
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Release : 2013-04-17
Genre : Mathematics
Kind : eBook
Book Rating : 546/5 ( reviews)

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Book Synopsis A Course in p-adic Analysis by : Alain M. Robert

Download or read book A Course in p-adic Analysis written by Alain M. Robert. This book was released on 2013-04-17. Available in PDF, EPUB and Kindle. Book excerpt: 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.

P-adic Analysis

1980-11-28 Mathematics
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Release : 1980-11-28
Genre : Mathematics
Kind : eBook
Book Rating : 605/5 ( reviews)

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Book Synopsis P-adic Analysis by : Neal Koblitz

Download or read book P-adic Analysis written by Neal Koblitz. This book was released on 1980-11-28. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.

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.

The Riemann Zeta-Function

2011-05-03 Mathematics
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Release : 2011-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 146/5 ( reviews)

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Book Synopsis The Riemann Zeta-Function by : Anatoly A. Karatsuba

Download or read book The Riemann Zeta-Function written by Anatoly A. Karatsuba. This book was released on 2011-05-03. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

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