P Adic Analysis Compared With Real 1 E
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P Adic Analysis Compared With Real 1 E
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Author : Svetlana Katok
language : en
Publisher:
Release Date : 2007
P Adic Analysis Compared With Real 1 E written by Svetlana Katok and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
P Adic Analysis Compared With Real
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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.
P Adic Analysis And Mathematical Physics
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Author : V S Vladimirov
language : en
Publisher: World Scientific
Release Date : 1994-04-28
P Adic Analysis And Mathematical Physics written by V S Vladimirov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-04-28 with Mathematics categories.
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.
Value Distribution In P Adic Analysis
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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.
A Course In P Adic Analysis
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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.
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 Numbers P Adic Analysis And Zeta Functions
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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.
These lecture notes are intended as an introduction to p-adic analysis on the elementary level. For this reason they presuppose as little background as possi ble. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topolog ical spaces. The purpose of this book is twofold: to develop some basic ideas of p-adic analysis, and to present two striking applications which, it is hoped, can be as effective pedagogically as they were historically in stimulating interest in the field. The first of these applications is presented in Chapter II, since it only requires the most elementary properties of Q ; this is Mazur's construction by p means of p-adic integration of the Kubota-Leopoldtp-adic zeta-function, which "p-adically interpolates" the values of the Riemann zeta-function at the negative odd integers. My treatment is based on Mazur's Bourbaki notes (unpublished).
P Adic Analysis
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Author : Francesco Baldassari
language : en
Publisher:
Release Date : 2014-09-01
P Adic Analysis written by Francesco Baldassari and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
P Adic Numbers
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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 Function Analysis
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Author : Jose M. Bayod
language : en
Publisher: CRC Press
Release Date : 2020-12-17
P Adic Function Analysis written by Jose M. Bayod and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-17 with Mathematics categories.
"Written by accomplished and well-known researchers in the field, this unique volume discusses important research topics on p-adic functional analysis and closely related areas, provides an authoritative overview of the main investigative fronts where developments are expected in the future, and more. "
P Adic Analysis
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Author : Neal Koblitz
language : en
Publisher: Cambridge University Press
Release Date : 1980-11-28
P Adic Analysis written by Neal Koblitz 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 1980-11-28 with Mathematics categories.
An introduction to recent work in the theory of numbers and its interrelation with algebraic geometry and analysis.