Dr schikhof is able to point out and explain how p adic and real analysis differ. These exotic numbers or so they appeared at first are now wellestablished in the mathematical world and used more and more by physicists as well. It gives an elementary and thoroughly written introduction to p adic numbers and padic analysis with great numbers of examples as well as applications of p adic numbers in classical mechanics, dynamical systems, quantum mechanics. The book provides comprehensive coverage on p adic numbers and analytic functions, integration theory, the gaussian integrals, fourier transformation. In, the behavior of a trajectory of a rational p adic dynamical system in a complex p adic field c p is studied. So the p adic absolute value of x2q is small when the numerator of xis divisible by a high power of p, and it is large when the denominator of xis. The p adic absolute value on q is given by jxj p 0 if x 0, p vpx otherwise.
Asia pacific mathematics newsletter what are padic. Lately p adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the nonarchimedean geometry of spacetime at small distances. The p adic numbers are an intuitive arithmetic system but geometrically counterintuitive that was discovered by german mathematician kurt hensel in about 1899 and by german mathematician ernst kummer18101893. Books on p adic numbers and padic analysis usually reflect quite closely the interests and concerns of their authors. This elementary introduction offers a broad understanding of p adic numbers. In mathematics, padic analysis is a branch of number theory that deals with the mathematical analysis of functions of p adic numbers the theory of complexvalued numerical functions on the p adic numbers is part of the theory of locally compact groups.
Zelenov, p adic analysis and mathematical physics world scientific publishing i. A catalogue record for this book is available from the british library. This is the first book to deal with applications of p adic numbers in theoretical and. Hensel 1904 in connection with problems of the pure theory of numbers. As a consequence, this book will become a standard reference for professionals especially in p adic analysis, number theory and algebraic geometry and will be welcomed as a textbook for advanced students of mathematics familiar with algebra and analysis. To do mathematical analysis, one needs a completion of the field q of. It gives an elementary and thoroughly written introduction. This is the first book to deal with applications of p adic numbers in theoretical. Ja61 minkowski measurabilitiy and exact fractal tube formulas for p adic selfsimilar strings, contemporary mathematics, american mathematical society, 600 20, p.
It emerged in 1987 as a result of efforts to find a nonarchimedean approach to the spacetime and string dynamics at the planck scale, but then was extended to many. Jan 01, 2021 the employment of p adic mathematics in theoretical physics is in the active stage of modeling some physical processes with the development of related p adic methods, known as p adic mathematical physics see books vladimirov et al. Pdf on measurements, numbers and padic mathematical. Read download p adic numbers an introduction universitext pdf. Traditionally mathematical physics has been quite closely associated to ideas in calculus, particularly those of differential equations. Asia pacific mathematics newsletter what are padic numbers. Padic numbers, padic analysis, and zetafunctions springerverlag, berlin, 1984.
By a concept of adelic string one can unify and simultaneously study. This approach guarantees the reader quickly becomes acquainted with this equally real analysis and appreciates its relevance. Analysis of business connections utilizing theory of topology of random graphs in padic mathematical physics, khrennikov, z. We prove the local solvability of the padic analog of the navierstokes equation. The book gives an introduction to \ p \ adic numbers from the point of view of number theory, topology, and analysis. Amsip studies in advanced mathematics, issn 10893288. Neal koblitz treats the shnirelman integral in his book p adic analysis. Pseudodifferential operators and wavelets over real and p adic fields by nguyen minh chuong, pseudodifferential operators and wavelets over real and p adic fields books available in pdf, epub, mobi format. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include. Volovich, number theory as the ultimate physical theory, p adic numbers, ultrametric analysis and applications 2 2010 7787 abstract at the planck scale doubt is cast on the usual notion of spacetime and one cannot think about elementary particles. Then jaj 2 2, jaj 3 3 8, jaj 5 53, jaj p 1 for p 7.
Read download p adic numbers an introduction universitext. Free mathematical physics books download ebooks online. This book offers a selfcontained presentation of basic padic analysis. P adic analysis and mathematical physics series on soviet. Series on soviet and east european mathematics p adic analysis and mathematical physics, pp. May 23, 2012 p adic strings are important objects of string theory, as well as of p adic mathematical physics and nonlocal cosmology. It is perhaps the most suitable text for beginners, and i shall definitely recommend it to anyone who asks me. P adic quantum mechanics is a relatively recent approach to understanding the nature of fundamental physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and intelligible manner.
This relatively recent theory has become increasingly important in the last decade with exciting applications in a variety of fields, including biology, image analysis, psychology, and information science. This is an introduction to p adic analysis which is elementary yet complete and which displays the variety of applications of the subject. This is the first book to deal with applications of padic numbers in theoretical and mathematical physics. Pdf p adic numbers an introduction universitext download full. Kurt hensel 18611941 discovered the p adic numbers around the turn of the century. It is the application of padic analysis to quantum mechanics.
This is the first book to deal with applications of p adic numbers in theoretical and mathematical physics. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. What are p adic numbers, p adic analysis, p adic physics, p adic probability. Number theorists tend to emphasize the algebraic side and to focus on results that show up in their work. The average period from submission to first decision in 2019 was 60 days, and that from first decision to acceptance was 23 days. System upgrade on fri, jun 26th, 2020 at 5pm et during this period, our website will be offline for less than an hour but the ecommerce and registration of new users may not be available for up to 4 hours. Buy padic functional analysis volume 192 lecture notes in pure and applied mathematics on free shipping on qualified orders padic functional analysis volume 192 lecture notes in pure and applied mathematics. Presents the proceedings of the 2nd international conference on p adic mathematical physics, held in belgrade, serbia and montenegro, 1521 september 2005. 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. Let me sketch this proof in comparison with weils program of proving his conjecture. Partial differential equations of mathematical physics pdf 105p this note aims to make students aware of the physical origins of the main partial differential equations of classical mathematical physics, including the fundamental equations of fluid and solid mechanics, thermodynamics, and. Please join the simons foundation and our generous member organizations in supporting arxiv during our giving campaign september 2327. I tried to select only the works in book formats, real books that are mainly in pdf format, so many wellknown htmlbased mathematics web pages and online tutorials are left out.
Apr 27, 2009 tion to some aspects of padic mathematical physics could be helpful for the readers of the. Symmetry in mathematics and physics conference join us in celebrating professor varadarajans 70th birthday. Theory of p adic valued functions is exposed in the schikhof book 8. Some remarks about applications of p adic numbers to mathematics, biology and physics are given. On padic and adelic generalization of quantum field theory. P adic analysis and mathematical physics series on soviet and. But recently new models of the quantum physics were proposed on the basis of p adic numbers field qp. Feb 15, 20 the basics of p adic analysis and of p adic mathematical physics are explained in.
The paper studies siegel disks and attractors of those dynamical systems. Padic analysis wikimili, the best wikipedia reader. Series of functions, binomial theorem, series expansion of functions, vectors, complex functions, derivatives, intergrals, and the delta function, determinants, matrices, vector analysis, vector differentiation and integration, integral theorems and potential theory, curvilinear coordinates, tensor. This text is a selfcontained presentation of basic p adic analysis with a focus on analytic topics. Padic analysis and mathematical physics soviet and east. Varadarajans research has always been motivated by a desire to understand the role of symmetry in mathematics and physics. In mathematics, padic analysis is a branch of number theory that deals with the mathematical analysis of functions of p adic numbers. Download pseudodifferential operators and wavelets over real and p adic fields books, this monograph offers a selfcontained introduction to pseudodifferential operators and wavelets over real and p adic fields. Mathematics and physics are traditionally very closely linked subjects. The 3 adic integers, with selected corresponding characters on their pontryagin dual group. Introduction to padic analytic number theory american. Here is an unordered list of online mathematics books, textbooks, monographs, lecture notes, and other mathematics related documents freely available on the web. Pdf p adic numbers an introduction universitext download.
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. Pdf on measurements, numbers and padic mathematical physics. Front matter padic analysis and mathematical physics. Padic numbers, padic analysis, and zetafunctions cep. Buy padic analysis and mathematical physics soviet and east european mathematics on.
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