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Author: S. Albeverio
Publisher: Cambridge University Press
Published: 2010-03-18
Total Pages: 369
ISBN-13: 0521148561
DOWNLOAD EBOOKA wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Author: Sergio Albeverio
Publisher:
Published: 2010
Total Pages: 351
ISBN-13: 9781139122856
DOWNLOAD EBOOKA wide-ranging survey of new and important topics in p-adic analysis for researchers and graduate students.
Author: Sergio Albeverio
Publisher:
Published: 2014-05-14
Total Pages: 368
ISBN-13: 9781139127776
DOWNLOAD EBOOKA wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.
Author: Andrei Y. Khrennikov
Publisher: Springer Science & Business Media
Published: 2013-03-09
Total Pages: 271
ISBN-13: 9401583560
DOWNLOAD EBOOKNumbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I· We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo· These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.
Author: Alain Escassut
Publisher: World Scientific
Published: 2015-11-27
Total Pages: 559
ISBN-13: 9814730122
DOWNLOAD EBOOKThe 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.
Author: Vasili? Sergeevich Vladimirov
Publisher: World Scientific
Published: 1994
Total Pages: 350
ISBN-13: 9789810208806
DOWNLOAD EBOOKp-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: Andrei Y. Khrennikov
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 279
ISBN-13: 1402026609
DOWNLOAD EBOOKThis 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.
Author: Kiran S. Kedlaya
Publisher: Cambridge University Press
Published: 2010-06-10
Total Pages: 399
ISBN-13: 1139489208
DOWNLOAD EBOOKOver 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: M. Ram Murty
Publisher: American Mathematical Soc.
Published: 2009-02-09
Total Pages: 162
ISBN-13: 0821847740
DOWNLOAD EBOOKThis 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: Helge Glöckner
Publisher: American Mathematical Soc.
Published: 2016-05-20
Total Pages: 346
ISBN-13: 1470419882
DOWNLOAD EBOOKThis volume contains the Proceedings of the 13th International Conference on p-adic Functional Analysis, held from August 12–16, 2014, at the University of Paderborn, Paderborn, Germany. The articles included in this book feature recent developments in various areas of non-Archimedean analysis, non-Archimedean functional analysis, representation theory, number theory, non-Archimedean dynamical systems and applications. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-Archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
