Download Full eBooks in PDF
Introduction To P Adic Numbers And Valuation Theory Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Introduction To P Adic Numbers And Valuation Theory book. This book definitely worth reading, it is an incredibly well-written.
Author : George Bachman
Publisher : Unknown
Page : 196 pages
File Size : 44,5 Mb
Release : 1964
Category : Algebraic fields
ISBN : UOM:39015065682224
Author : Fernando Q. Gouvea
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 53,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662222782
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 : Paulo Ribenboim
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 44,5 Mb
Release : 1999-05-21
Category : Mathematics
ISBN : 0387985255
Valuation theory is used constantly in algebraic number theory and field theory, and is currently gaining considerable research interest. Ribenboim fills a unique niche in the literature as he presents one of the first introductions to classical valuation theory in this up-to-date rendering of the authors long-standing experience with the applications of the theory. The presentation is fully up-to-date and will serve as a valuable resource for students and mathematicians.
Author : Kurt Mahler
Publisher : CUP Archive
Page : 114 pages
File Size : 48,7 Mb
Release : 1973-03-29
Category : Mathematics
ISBN : 8210379456XXX
Author : Fernando Q. Gouvêa
Publisher : Springer Nature
Page : 366 pages
File Size : 40,8 Mb
Release : 2020-06-19
Category : Mathematics
ISBN : 9783030472955
There are numbers of all kinds: rational, real, complex, p-adic. The p-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers. From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE
Author : NEAL Koblitz
Publisher : Springer Science & Business Media
Page : 134 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468400472
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).
Author : S. Albeverio,V. M. Shelkovich
Publisher : Cambridge University Press
Page : 369 pages
File Size : 53,9 Mb
Release : 2010-03-18
Category : Mathematics
ISBN : 9780521148566
A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Author : Svetlana Katok
Publisher : American Mathematical Soc.
Page : 170 pages
File Size : 40,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9780821842201
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 : Alain M. Robert
Publisher : Springer Science & Business Media
Page : 464 pages
File Size : 42,8 Mb
Release : 2000-05-31
Category : Mathematics
ISBN : 0387986693
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 : Lawrence Narici
Publisher : CRC Press
Page : 212 pages
File Size : 53,7 Mb
Release : 1971-06-01
Category : Mathematics
ISBN : 0824714849
This book presents functional analysis over arbitrary valued fields and investigates normed spaces and algebras over fields with valuation, with attention given to the case when the norm and the valuation are nonarchimedean. It considers vector spaces over fields with nonarchimedean valuation.
Author : Otto Endler
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642655050
These are the revised notes of a course for graduate students and some seminar talks which I gave at the University of Rochester during Fall Term 1969/70. They would not have been written without the encouragement and the aid which I received, during all stages of the work, by friends from Rochester, Rio de Janeiro, and Bonn. I wish to thank all of them: Barbara Grabkowicz encouraged me to write these notes in English and read carefully parts of a preliminary manuscript, as did Gervasio G. Bastos, Yves A. E. Lequain, Walter Strubel, and Antonio J. Engler. Many valuable suggestions were given me by Yves A. E. Lequain, and several improvements of theorems and proofs are due to him. I am particularly grateful to Linda C. Hill for her criticism in reading the last version and for improving and smoothing many of my formulations. Last but not least I thank Wilson Goes for the excellent typing. Most of this book was elaborated when I stayed in Rio de Janeiro as a Visiting Professor at IMPA (Institute for Pure and Applied Mathematics) and as a Pesquisador-Conferencista of CNPq (National Research Council). Thanks are also due to these institu tions.
Author : Claire C. Ralph,Santiago R. Simanca
Publisher : Cambridge University Press
Page : 146 pages
File Size : 47,7 Mb
Release : 2012-01-26
Category : Mathematics
ISBN : 9781107674141
This complete introduction to the study of arithmetic differential operators over the p-adic integers offers graduate students and researchers an accessible guide to this novel and promising area of mathematics. It starts with the basics and is accessible to anyone with a basic grasp of algebraic number theory.
Author : Andrew Schumann
Publisher : Springer
Page : 468 pages
File Size : 49,7 Mb
Release : 2018-05-25
Category : Technology & Engineering
ISBN : 9783319915425
This book presents fundamental theoretical results for designing object-oriented programming languages for controlling swarms. It studies the logics of swarm behaviours. According to behaviourism, all behaviours can be controlled or even managed by stimuli in the environment: attractants (motivational reinforcement) and repellents (motivational punishment). At the same time, there are two main stages in reactions to stimuli: sensing (perceiving signals) and motoring (appropriate direct reactions to signals). This book examines the strict limits of behaviourism from the point of view of symbolic logic and algebraic mathematics: how far can animal behaviours be controlled by the topology of stimuli? On the one hand, we can try to design reversible logic gates in which the number of inputs is the same as the number of outputs. In this case, the behaviouristic stimuli are inputs in swarm computing and appropriate reactions at the motoring stage are its outputs. On the other hand, the problem is that even at the sensing stage each unicellular organism can be regarded as a logic gate in which the number of outputs (means of perceiving signals) greatly exceeds the number of inputs (signals).
Author : Demeter Krupka
Publisher : Elsevier
Page : 500 pages
File Size : 49,7 Mb
Release : 2000-04-01
Category : Mathematics
ISBN : 0080954162
This book provides a comprehensive introduction to modern global variational theory on fibred spaces. It is based on differentiation and integration theory of differential forms on smooth manifolds, and on the concepts of global analysis and geometry such as jet prolongations of manifolds, mappings, and Lie groups. The book will be invaluable for researchers and PhD students in differential geometry, global analysis, differential equations on manifolds, and mathematical physics, and for the readers who wish to undertake further rigorous study in this broad interdisciplinary field. Featured topics - Analysis on manifolds - Differential forms on jet spaces - Global variational functionals - Euler-Lagrange mapping - Helmholtz form and the inverse problem - Symmetries and the Noether’s theory of conservation laws - Regularity and the Hamilton theory - Variational sequences - Differential invariants and natural variational principles - First book on the geometric foundations of Lagrange structures - New ideas on global variational functionals - Complete proofs of all theorems - Exact treatment of variational principles in field theory, inc. general relativity - Basic structures and tools: global analysis, smooth manifolds, fibred spaces
Author : Antonio J. Engler,Alexander Prestel
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 47,7 Mb
Release : 2005-12-28
Category : Mathematics
ISBN : 9783540300359
Absolute values and their completions – such as the p-adic number fields – play an important role in number theory. Krull's generalization of absolute values to valuations made possible applications in other branches of mathematics. In valuation theory, the notion of completion must be replaced by that of "Henselization". This book develops the theory of valuations as well as of Henselizations, based on the skills of a standard graduate course in algebra.