Arithmetic Differential Operators Over The P Adic Integers
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Arithmetic Differential Operators Over the P-adic Integers
Author: Claire C. Ralph
language: en
Publisher: Cambridge University Press
Release Date: 2012-01-26
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.
P-adic Analysis and Mathematical Physics
Author: Vasili? Sergeevich Vladimirov
language: en
Publisher: World Scientific
Release Date: 1994
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.
p-adic Differential Equations
Author: Kiran S. Kedlaya
language: en
Publisher: Cambridge University Press
Release Date: 2010-06-10
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.