P Adic Differential Equations

Author : Kiran S. Kedlaya
Publisher : Cambridge University Press
ISBN 13 : 1139489208
Total Pages : 399 pages
Book Rating : 4.01/5 ( download)

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Download or read book p-adic Differential Equations written by Kiran S. Kedlaya and published by Cambridge University Press. This book was released on 2010-06-10 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1461381932
Total Pages : 318 pages
Book Rating : 4.38/5 ( download)

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Download or read book Lectures on p-adic Differential Equations written by Bernard Dwork and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 : 9780511750182
Total Pages : 400 pages
Book Rating : 4.88/5 ( download)

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Download or read book P-adic Differential Equations written by Kiran Sridhara Kedlaya and published by . This book was released on 2014-05-14 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive, unified development of the theory of p-adic differential equations.

Author : Alain M. Robert
Publisher : Springer Science & Business Media
ISBN 13 : 1475732546
Total Pages : 451 pages
Book Rating : 4.42/5 ( download)

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Download or read book A Course in p-adic Analysis written by Alain M. Robert and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 451 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9789810208806
Total Pages : 350 pages
Book Rating : 4.04/5 ( download)

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Download or read book P-adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Kiran Kedlaya
Publisher : Cambridge University Press
ISBN 13 : 1009123343
Total Pages : 517 pages
Book Rating : 4.41/5 ( download)

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Download or read book p-adic Differential Equations written by Kiran Kedlaya and published by Cambridge University Press. This book was released on 2022-06-09 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed and unified treatment of $P$-adic differential equations, from the basic principles to the current frontiers of research.

Author : A.K. Katsaras
Publisher : CRC Press
ISBN 13 : 0203908147
Total Pages : 337 pages
Book Rating : 4.43/5 ( download)

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Download or read book P-Adic Functional Analysis written by A.K. Katsaras and published by CRC Press. This book was released on 2001-07-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
ISBN 13 :
Total Pages : pages
Book Rating : 4.99/5 ( download)

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Download or read book On P-adic Differential Equations on Semistable Varieties written by Valentina Di Proietto and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bernard Dwork
Publisher : Princeton University Press
ISBN 13 : 0691036810
Total Pages : 348 pages
Book Rating : 4.16/5 ( download)

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Download or read book An Introduction to G-functions written by Bernard Dwork and published by Princeton University Press. This book was released on 1994-05-22 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : S. Albeverio
Publisher : Cambridge University Press
ISBN 13 : 0521148561
Total Pages : 369 pages
Book Rating : 4.66/5 ( download)

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Download or read book Theory of P-adic Distributions written by S. Albeverio and published by Cambridge University Press. This book was released on 2010-03-18 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: A wide-ranging 2010 survey of new and important topics in p-adic analysis for researchers and graduate students.