A Course In P Adic Analysis

Author : Alain M. Robert
Publisher : Springer Science & Business Media
ISBN 13 : 1475732546
Total Pages : 451 pages
Book Rating : 4.42/5 ( download)

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Download or read book A Course in p-adic Analysis written by Alain M. Robert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 451 pages. 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.

Author : Alain M. Robert
Publisher : Springer Science & Business Media
ISBN 13 : 9780387986692
Total Pages : 464 pages
Book Rating : 4.93/5 ( download)

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Download or read book A Course in p-adic Analysis written by Alain M. Robert and published by Springer Science & Business Media. This book was released on 2000-05-31 with total page 464 pages. 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.

Author : Svetlana Katok
Publisher : American Mathematical Soc.
ISBN 13 : 082184220X
Total Pages : 170 pages
Book Rating : 4.01/5 ( download)

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Download or read book $p$-adic Analysis Compared with Real written by Svetlana Katok and published by American Mathematical Soc.. This book was released on 2007 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
ISBN 13 : 3662222787
Total Pages : 285 pages
Book Rating : 4.82/5 ( download)

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Download or read book p-adic Numbers written by Fernando Q. Gouvea and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 285 pages. 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.

Author : Neal Koblitz
Publisher : Springer Science & Business Media
ISBN 13 : 1461211123
Total Pages : 163 pages
Book Rating : 4.29/5 ( download)

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Download or read book p-adic Numbers, p-adic Analysis, and Zeta-Functions written by Neal Koblitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 163 pages. 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.

Author : Kiran S. Kedlaya
Publisher : Cambridge University Press
ISBN 13 : 1139489208
Total Pages : 399 pages
Book Rating : 4.01/5 ( download)

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Download or read book p-adic Differential Equations written by Kiran S. Kedlaya and published by Cambridge University Press. This book was released on 2010-06-10 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.

Author : Neal Koblitz
Publisher : Cambridge University Press
ISBN 13 : 0521280605
Total Pages : 171 pages
Book Rating : 4.00/5 ( download)

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Download or read book P-adic Analysis written by Neal Koblitz and published by Cambridge University Press. This book was released on 1980-11-28 with total page 171 pages. 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.

Author : M. Ram Murty
Publisher : American Mathematical Soc.
ISBN 13 : 0821847740
Total Pages : 162 pages
Book Rating : 4.49/5 ( download)

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Download or read book Introduction to $p$-adic Analytic Number Theory written by M. Ram Murty and published by American Mathematical Soc.. This book was released on 2009-02-09 with total page 162 pages. 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.

Author : Vasili? Sergeevich Vladimirov
Publisher : World Scientific
ISBN 13 : 9789810208806
Total Pages : 350 pages
Book Rating : 4.04/5 ( download)

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Download or read book P-adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. 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.

Author : Peter Scholze
Publisher : Princeton University Press
ISBN 13 : 0691202095
Total Pages : 260 pages
Book Rating : 4.99/5 ( download)

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Download or read book Berkeley Lectures on P-adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.