A Course in p-adic Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook A Course in p-adic Analysis write by Alain M. Robert. This book was released on 2013-04-17. A Course in p-adic Analysis available in PDF, EPUB and Kindle. 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 Compared with Real
$p$-adic Analysis Compared with Real - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook $p$-adic Analysis Compared with Real write by Svetlana Katok. This book was released on 2007. $p$-adic Analysis Compared with Real available in PDF, EPUB and Kindle. 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.
p-adic Numbers
p-adic Numbers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook p-adic Numbers write by Fernando Q. Gouvea. This book was released on 2013-06-29. p-adic Numbers available in PDF, EPUB and Kindle. 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, p-adic Analysis, and Zeta-Functions
p-adic Numbers, p-adic Analysis, and Zeta-Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook p-adic Numbers, p-adic Analysis, and Zeta-Functions write by Neal Koblitz. This book was released on 2012-12-06. p-adic Numbers, p-adic Analysis, and Zeta-Functions available in PDF, EPUB and Kindle. 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.
Introduction to $p$-adic Analytic Number Theory
Introduction to $p$-adic Analytic Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to $p$-adic Analytic Number Theory write by M. Ram Murty. This book was released on 2009-02-09. Introduction to $p$-adic Analytic Number Theory available 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.
