Arithmetic Differential Operators Over the P-adic Integers PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Arithmetic Differential Operators Over the P-adic Integers PDF full book. Access full book title Arithmetic Differential Operators Over the P-adic Integers by Claire C. Ralph. Download full books in PDF and EPUB format.
Author: Claire C. Ralph
Publisher: Cambridge University Press
ISBN: 110767414X
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
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: Claire C. Ralph
Publisher: Cambridge University Press
ISBN: 110767414X
Category : Mathematics
Languages : en
Pages : 146
Get Book Here
Book Description
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: Bernard Dwork
Publisher: Springer Science & Business Media
ISBN: 1461381932
Category : Mathematics
Languages : en
Pages : 318
Get Book Here
Book Description
The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx + (c(l - x) + (c - 1 - a - b)x) dx - ab)y = 0, 2 with a, b, c in 4) n Zp, by constructing the associated Frobenius structure. For this construction we draw upon the methods of Alan Adolphson [1] in his 1976 work on Hecke polynomials. We are also indebted to him for the account (appearing as an appendix) of the relation between this differential equation and certain L-functions. We are indebted to G. Washnitzer for the method used in the construction of our dual theory (Chapter 2). These notes represent an expanded form of lectures given at the U. L. P. in Strasbourg during the fall term of 1980. We take this opportunity to thank Professor R. Girard and IRMA for their hospitality. Our subject-p-adic analysis-was founded by Marc Krasner. We take pleasure in dedicating this work to him. Contents 1 Introduction . . . . . . . . . . 1. The Space L (Algebraic Theory) 8 2. Dual Theory (Algebraic) 14 3. Transcendental Theory . . . . 33 4. Analytic Dual Theory. . . . . 48 5. Basic Properties of", Operator. 73 6. Calculation Modulo p of the Matrix of ~ f,h 92 7. Hasse Invariants . . . . . . 108 8. The a --+ a' Map . . . . . . . . . . . . 110 9. Normalized Solution Matrix. . . . . .. 113 10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities. . . . . . . . . . . . . 137 11. Second-Order Linear Differential Equations Modulo Powers ofp ..... .
Author: A.K. Katsaras
Publisher: CRC Press
ISBN: 9780203908143
Category : Mathematics
Languages : en
Pages : 340
Get Book Here
Book Description
This volume collects together lectures presented at the Sixth International Conference held at the University of Ioannina, Greece, on p-adic functional analysis with applications in the fields of physics, differential equations, number theory, probability theory, dynamical systems, and algebraic number fields. It discusses the commutation relation AB-BA=I and its central role in quantum mechanics.
Author: Kiran S. Kedlaya
Publisher: Cambridge University Press
ISBN: 1139489208
Category : Mathematics
Languages : en
Pages : 399
Get Book Here
Book Description
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.
Author: Vasili? Sergeevich Vladimirov
Publisher: World Scientific
ISBN: 9789810208806
Category : Science
Languages : en
Pages : 350
Get Book Here
Book Description
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.
Author: Kurt Mahler
Publisher: CUP Archive
ISBN:
Category : Mathematics
Languages : en
Pages : 114
Get Book Here
Book Description
Author: Thomas J. Bridges
Publisher: Cambridge University Press
ISBN: 1107565561
Category : Mathematics
Languages : en
Pages : 299
Get Book Here
Book Description
A range of experts contribute introductory-level lectures on active topics in the theory of water waves.
Author: Pieter Belmans
Publisher: Cambridge University Press
ISBN: 1009054856
Category : Mathematics
Languages : en
Pages : 307
Get Book Here
Book Description
A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.
Author: C. T. J. Dodson
Publisher: Cambridge University Press
ISBN: 1316601951
Category : Mathematics
Languages : en
Pages : 315
Get Book Here
Book Description
A new approach to studying Fréchet geometry using projective limits of geometrical objects modelled on Banach spaces.
Author: Edgard A. Pimentel
Publisher: Cambridge University Press
ISBN: 1009096664
Category : Mathematics
Languages : en
Pages : 203
Get Book Here
Book Description
A modern account of elliptic regularity theory, with a rigorous presentation of recent developments for fundamental models.
