A Course In P Adic Analysis
DOWNLOAD
Download A Course In P Adic Analysis PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Course In P Adic Analysis book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
A Course In P Adic Analysis
DOWNLOAD
Author : Alain M. Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
A Course In P Adic Analysis written by Alain M. Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.
A Course In P Adic Analysis
DOWNLOAD
Author : Alain M. Robert
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-05-31
A Course In P Adic Analysis written by Alain M. Robert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-31 with Mathematics categories.
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
DOWNLOAD
Author : Svetlana Katok
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
P Adic Analysis Compared With Real written by Svetlana Katok and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
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.
A Course In P Adic Analysis
DOWNLOAD
Author : Alain M. Robert
language : en
Publisher:
Release Date : 2014-01-15
A Course In P Adic Analysis written by Alain M. Robert and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
P Adic Numbers P Adic Analysis And Zeta Functions
DOWNLOAD
Author : Neal Koblitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
P Adic Numbers P Adic Analysis And Zeta Functions written by Neal Koblitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Neal Koblitz was a student of Nicholas M. Katz, under whom he received his Ph.D. in mathematics at Princeton in 1974. He spent the year 1974 -75 and the spring semester 1978 in Moscow, where he did research in p -adic analysis and also translated Yu. I. Manin's "Course in Mathematical Logic" (GTM 53). He taught at Harvard from 1975 to 1979, and since 1979 has been at the University of Washington in Seattle. He has published papers in number theory, algebraic geometry, and p-adic analysis, and he is the author of "p-adic Analysis: A Short Course on Recent Work" (Cambridge University Press and GTM 97: "Introduction to Elliptic Curves and Modular Forms (Springer-Verlag).
Introduction To P Adic Analytic Number Theory
DOWNLOAD
Author : M. Ram Murty
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-02-09
Introduction To P Adic Analytic Number Theory written by M. Ram Murty and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Mathematics categories.
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.
P Adic Numbers
DOWNLOAD
Author : Fernando Q. Gouvea
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
P Adic Numbers written by Fernando Q. Gouvea and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
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 Differential Equations
DOWNLOAD
Author : Kiran S. Kedlaya
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-10
P Adic Differential Equations written by Kiran S. Kedlaya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-10 with Mathematics categories.
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.
Analytic Elements In P Adic Analysis
DOWNLOAD
Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 1995
Analytic Elements In P Adic Analysis written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
This is probably the first book dedicated to this topic. The behaviour of the analytic elements on an infraconnected set D in K an algebraically closed complete ultrametric field is mainly explained by the circular filters and the monotonous filters on D, especially the T-filters: zeros of the elements, Mittag-Leffler series, factorization, Motzkin factorization, maximum principle, injectivity, algebraic properties of the algebra of the analytic elements on D, problems of analytic extension, factorization into meromorphic products and connections with Mittag-Leffler series. This is applied to the differential equation y'=hy (y, h analytic elements on D), analytic interpolation, injectivity, and to the p-adic Fourier transform.
Value Distribution In P Adic Analysis
DOWNLOAD
Author : Alain Escassut
language : en
Publisher: World Scientific
Release Date : 2015-11-27
Value Distribution In P Adic Analysis written by Alain Escassut and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-27 with Mathematics categories.
The book first explains the main properties of analytic functions in order to use them in the study of various problems in p-adic value distribution. Certain properties of p-adic transcendental numbers are examined such as order and type of transcendence, with problems on p-adic exponentials. Lazard's problem for analytic functions inside a disk is explained. P-adic meromorphics are studied. Sets of range uniqueness in a p-adic field are examined. The ultrametric Corona problem is studied. Injective analytic elements are characterized. The p-adic Nevanlinna theory is described and many applications are given: p-adic Hayman conjecture, Picard's values for derivatives, small functions, branched values, growth of entire functions, problems of uniqueness, URSCM and URSIM, functions of uniqueness, sharing value problems, Nevanlinna theory in characteristic p>0, p-adic Yosida's equation.