Download or read book P adic Methods and Their Applications written by Serc Post-Doctoral Fellow Department of Mathematics Andrew J Baker and published by Oxford University Press on Demand. This book was released on 1992 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of texts have recently become available which provide good general introductions to p-Adic numbers and p-Adic analysis. However, there is at present a gap between such books and the sophisticated applications in the research literature. The aim of this book is to bridge this gulf byproviding a collection of intermediate level articles on various applications of p-Adic techniques throughout mathematics. The idea for producing such a volume was suggested by Oxford University Press in connection with a three day meeting `p-Adic Methods and their Applications' held at Manchester University in September 1989 and which have received financial support from the London Mathematical Society. Some of thesearticles grew out of talks given at this conference, others were written by invitation especially for this volume. All contributions were refereed with a particular view to their suitability for inclusion in such a book.
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.
Download or read book Ultrametric Pseudodifferential Equations and Applications written by Andrei Yu. Khrennikov and published by Cambridge University Press. This book was released on 2018-04-26 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.
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.
Download or read book Advances on Superelliptic Curves and Their Applications written by L. Beshaj and published by IOS Press. This book was released on 2015-07-16 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book had its origins in the NATO Advanced Study Institute (ASI) held in Ohrid, Macedonia, in 2014. The focus of this ASI was the arithmetic of superelliptic curves and their application in different scientific areas, including whether all the applications of hyperelliptic curves, such as cryptography, mathematical physics, quantum computation and diophantine geometry, can be carried over to the superelliptic curves. Additional papers have been added which provide some background for readers who were not at the conference, with the intention of making the book logically more complete and easier to read, but familiarity with the basic facts of algebraic geometry, commutative algebra and number theory are assumed. The book is divided into three sections. The first part deals with superelliptic curves with regard to complex numbers, the automorphisms group and the corresponding Hurwitz loci. The second part of the book focuses on the arithmetic of the subject, while the third addresses some of the applications of superelliptic curves.
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.
Download or read book p adic Numbers written by Fernando Q. Gouvêa and published by Springer Nature. This book was released on 2020-06-19 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Recurrence Sequences written by Graham Everest and published by American Mathematical Soc.. This book was released on 2015-09-03 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recurrence sequences are of great intrinsic interest and have been a central part of number theory for many years. Moreover, these sequences appear almost everywhere in mathematics and computer science. This book surveys the modern theory of linear recurrence sequences and their generalizations. Particular emphasis is placed on the dramatic impact that sophisticated methods from Diophantine analysis and transcendence theory have had on the subject. Related work on bilinear recurrences and an emerging connection between recurrences and graph theory are covered. Applications and links to other areas of mathematics are described, including combinatorics, dynamical systems and cryptography, and computer science. The book is suitable for researchers interested in number theory, combinatorics, and graph theory.
Download or read book p adic Numbers written by Fernando Quadros Gouvea and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book An Introduction to Sieve Methods and Their Applications written by Alina Carmen Cojocaru and published by Cambridge University Press. This book was released on 2005-12-08 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rather than focus on the technical details which can obscure the beauty of sieve theory, the authors focus on examples and applications, developing the theory in parallel.
Download or read book p Adic Methods in Number Theory and Algebraic Geometry written by Alan Adolphson and published by American Mathematical Soc.. This book was released on 1992 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two meetings of the AMS in the autumn of 1989 - one at the Stevens Institute of Technology and the other at Ball State University - included Special Sessions on the role of p-adic methods in number theory and algebraic geometry. This volume grew out of these Special Sessions. Drawn from a wide area of mathematics, the articles presented here provide an excellent sampling of the broad range of trends and applications in p-adic methods.
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: Historical introduction Bernoulli numbers $p$-adic numbers Hensel's lemma $p$-adic interpolation $p$-adic $L$-functions $p$-adic integration Leopoldt's formula for $L_p(1,\chi)$ Newton polygons An introduction to Iwasawa theory Bibliography Index
Download or read book P adic Deterministic and Random Dynamics written by Andrei Y. Khrennikov and published by Springer Science & Business Media. This book was released on 2004-10-18 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the theory of p-adic (and more general non-Archimedean) dynamical systems. The main part of the book is devoted to discrete dynamical systems. It presents a model of probabilistic thinking on p-adic mental space based on ultrametric diffusion. Coverage also details p-adic neural networks and their applications to cognitive sciences: learning algorithms, memory recalling.
Download or read book Valuation Theory and Its Applications written by Franz-Viktor Kuhlmann and published by American Mathematical Soc.. This book was released on 2002-01-01 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two proceedings volumes stemming from the International Conference and Workshop on Valuation Theory held at the University of Saskatchewan (Saskatoon, SK, Canada). Valuation theory arose in the early part of the twentieth century in connection with number theory and has many important applications to geometry and analysis: the classical application to the study of algebraic curves and to Dedekind and Prufer domains; the close connection to the famousresolution of the singularities problem; the study of the absolute Galois group of a field; the connection between ordering, valuations, and quadratic forms over a formally real field; the application to real algebraic geometry; the study of noncommutative rings; etc. The special feature of this book isits focus on current applications of valuation theory to this broad range of topics. Also included is a paper on the history of valuation theory. The book is suitable for graduate students and research mathematicians working in algebra, algebraic geometry, number theory, and mathematical logic.
Download or read book Abelian Group Theory written by László Fuchs and published by American Mathematical Soc.. This book was released on 1989 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The traditional biennial international conference of abelian group theorists was held in August, 1987 at the University of Western Australia in Perth. With some 40 participants from five continents, the conference yielded a variety of papers indicating the healthy state of the field and showing the significant advances made in many areas since the last such conference in Oberwolfach in 1985. This volume brings together the papers presented at the Perth conference, together with a few others submitted by those unable to attend. The first section of the book is concerned with the structure of $p$-groups. It begins with a survey on H. Ulm's contributions to abelian group theory and related areas and also describes the surprising interaction between set theory and the structure of abelian $p$-groups. Another group of papers focuses on automorphism groups and the endomorphism rings of abelian groups. The book also examines various aspects of torsion-free groups, including the theory of their structure and torsion-free groups with many automorphisms. After one paper on mixed groups, the volume closes with a group of papers dealing with properties of modules which generalize corresponding properties of abelian groups.
Download or read book International Digital Imaging Correlation Society written by Michael Sutton and published by Springer. This book was released on 2017-03-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection represents a single volume of technical papers presented at the Annual International DIC Society Conference and SEM Fall Conference organized by the Society for Experimental Mechanics and Sandia National Laboratories and held in Philadelphia, PA, November 7-10, 2016. The volume presents early findings from experimental, standards development and various other investigations concerning digital image correlation - an important area within Experimental Mechanics. The area of Digital Image Correlation has been an integral track within the SEM Annual Conference spearheaded by Professor Michael Sutton from the University of South Carolina. In 2016, the SEM and Sandia joined their collaborative strengths to launch a standing fall meeting focusing specifically on developments in the area of Digital Image Correlation. The contributed papers within this volume span numerous technical aspects of DIC including standards development for the industry.
Download or read book P adic Monodromy and the Birch and Swinnerton Dyer Conjecture written by Glenn Stevens and published by American Mathematical Soc.. This book was released on 1994 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: The workshop aimed to deepen understanding of the interdependence between p-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, p-adic uniformization theory, p-adic differential equations, and deformations of Gaels representations.
