Arithmetic Differential Operators Over The P Adic Integers

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Arithmetic Differential Operators Over The P Adic Integers

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Author : Claire C. Ralph
language : en
Publisher: Cambridge University Press
Release Date : 2012-01-26

Arithmetic Differential Operators Over The P Adic Integers written by Claire C. Ralph and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-26 with Mathematics categories.

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

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Author : Vasili? Sergeevich Vladimirov
language : en
Publisher: World Scientific
Release Date : 1994

P Adic Analysis And Mathematical Physics written by Vasili? Sergeevich Vladimirov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Science categories.

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

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Author : Kiran S. Kedlaya
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-10

P Adic Differential Equations written by Kiran S. Kedlaya and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-10 with Mathematics categories.

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.

P Adic Analysis

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Author : W. A. Zúñiga-Galindo
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-12-02

P Adic Analysis written by W. A. Zúñiga-Galindo and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-02 with Mathematics categories.

This book is intended to provide a fast, interdisciplinary introduction to the basic results of p-adic analysis and its connections with mathematical physics and applications. The book revolves around three topics: (1) p-adic heat equations and ultradiffusion; (2) fundamental solutions and local zeta functions, Riesz kernels, and quadratic forms; (3) Sobolev-type spaces and pseudo-differential evolution equations. These topics are deeply connected with very relevant current research areas. The book includes numerous examples, exercises, and snapshots of several mathematical theories. This book arose from the need to quickly introduce mathematical audience the basic concepts and techniques to do research in p-adic analysis and its connections with mathematical physics and other areas. The book is addressed to a general mathematical audience, which includes computer scientists, theoretical physicists, and people interested in mathematical analysis, PDEs, etc.

Lectures On P Adic Differential Equations

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Author : Bernard Dwork
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Lectures On P Adic Differential Equations written by Bernard Dwork and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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 ..... .

Arithmetic And Geometry

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Author : Luis Dieulefait
language : en
Publisher: Cambridge University Press
Release Date : 2015-10-08

Arithmetic And Geometry written by Luis Dieulefait and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.

The world's leading authorities describe the state of the art in Serre's conjecture and rational points on algebraic varieties.

Surveys In Combinatorics 2015

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Author : Artur Czumaj
language : en
Publisher: Cambridge University Press
Release Date : 2015-07-02

Surveys In Combinatorics 2015 written by Artur Czumaj and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-02 with Mathematics categories.

This book contains surveys of recent important developments in combinatorics covering a wide range of areas in the field.

Arithmetic Differential Equations

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Author : Alexandru Buium
language : en
Publisher: American Mathematical Soc.
Release Date : 2005

Arithmetic Differential Equations written by Alexandru Buium and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.

Groups Graphs And Random Walks

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Author : Tullio Ceccherini-Silberstein
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-29

Groups Graphs And Random Walks written by Tullio Ceccherini-Silberstein and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-29 with Mathematics categories.

An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

Ultrametric Pseudodifferential Equations And Applications

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Author : Andreĭ I︠U︡rʹevich Khrennikov
language : en
Publisher: Cambridge University Press
Release Date : 2018-04-26

Ultrametric Pseudodifferential Equations And Applications written by Andreĭ I︠U︡rʹevich Khrennikov and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-26 with Mathematics categories.

Provides a novel interdisciplinary perspective on the state of the art of ultrametric pseudodifferential equations and their applications.