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Author | : Kiran S. Kedlaya |
Publisher | : Cambridge University Press |
Total Pages | : 399 |
Release | : 2010-06-10 |
Genre | : Mathematics |
ISBN | : 1139489208 |
Download p-adic Differential Equations Book in PDF, ePub and Kindle
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 | : Bernard Dwork |
Publisher | : Springer Science & Business Media |
Total Pages | : 318 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461381932 |
Download Lectures on p-adic Differential Equations Book in PDF, ePub and Kindle
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 | : Kiran Sridhara Kedlaya |
Publisher | : |
Total Pages | : 400 |
Release | : 2014-05-14 |
Genre | : Mathematics |
ISBN | : 9780511750182 |
Download P-adic Differential Equations Book in PDF, ePub and Kindle
The first comprehensive, unified development of the theory of p-adic differential equations.
Author | : Alain M. Robert |
Publisher | : Springer Science & Business Media |
Total Pages | : 451 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475732546 |
Download A Course in p-adic Analysis Book in PDF, ePub and Kindle
Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.
Author | : Vasili? Sergeevich Vladimirov |
Publisher | : World Scientific |
Total Pages | : 350 |
Release | : 1994 |
Genre | : Science |
ISBN | : 9789810208806 |
Download P-adic Analysis and Mathematical Physics Book in PDF, ePub and Kindle
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 | : A.K. Katsaras |
Publisher | : CRC Press |
Total Pages | : 337 |
Release | : 2001-07-03 |
Genre | : Mathematics |
ISBN | : 0203908147 |
Download P-Adic Functional Analysis Book in PDF, ePub and Kindle
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 | : Valentina Di Proietto |
Publisher | : |
Total Pages | : |
Release | : 2009 |
Genre | : |
ISBN | : |
Download On P-adic Differential Equations on Semistable Varieties Book in PDF, ePub and Kindle
Author | : Bernard Dwork |
Publisher | : Princeton University Press |
Total Pages | : 348 |
Release | : 1994-05-22 |
Genre | : Mathematics |
ISBN | : 0691036810 |
Download An Introduction to G-functions Book in PDF, ePub and Kindle
After presenting a review of valuation theory and elementary p-adic analysis together with an application to the congruence zeta function, this book offers a detailed study of the p-adic properties of formal power series solutions of linear differential equations. In particular, the p-adic radii of convergence and the p-adic growth of coefficients are studied. Recent work of Christol, Bombieri, André, and Dwork is treated and augmented. The book concludes with Chudnovsky's theorem: the analytic continuation of a G -series is again a G -series. This book will be indispensable for those wishing to study the work of Bombieri and André on global relations and for the study of the arithmetic properties of solutions of ordinary differential equations.
Author | : Sergiu Aizicovici |
Publisher | : CRC Press |
Total Pages | : 348 |
Release | : 2001-10-02 |
Genre | : Mathematics |
ISBN | : 9780203902189 |
Download Differential Equations And Control Theory Book in PDF, ePub and Kindle
Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equations over non-Archimedean fields in relation to Markov processes.
Author | : Vladimir G. Berkovich |
Publisher | : Princeton University Press |
Total Pages | : 164 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 0691128626 |
Download Integration of One-forms on P-adic Analytic Spaces. (AM-162) Book in PDF, ePub and Kindle
Among the many differences between classical and p-adic objects, those related to differential equations occupy a special place. For example, a closed p-adic analytic one-form defined on a simply-connected domain does not necessarily have a primitive in the class of analytic functions. In the early 1980s, Robert Coleman discovered a way to construct primitives of analytic one-forms on certain smooth p-adic analytic curves in a bigger class of functions. Since then, there have been several attempts to generalize his ideas to smooth p-adic analytic spaces of higher dimension, but the spaces considered were invariably associated with algebraic varieties. This book aims to show that every smooth p-adic analytic space is provided with a sheaf of functions that includes all analytic ones and satisfies a uniqueness property. It also contains local primitives of all closed one-forms with coefficients in the sheaf that, in the case considered by Coleman, coincide with those he constructed. In consequence, one constructs a parallel transport of local solutions of a unipotent differential equation and an integral of a closed one-form along a path so that both depend nontrivially on the homotopy class of the path. Both the author's previous results on geometric properties of smooth p-adic analytic spaces and the theory of isocrystals are further developed in this book, which is aimed at graduate students and mathematicians working in the areas of non-Archimedean analytic geometry, number theory, and algebraic geometry.