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Lectures on p-adic Differential Equations

  • Bernard Dwork

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 253)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Bernard Dwork
    Pages 1-7
  3. Bernard Dwork
    Pages 8-13
  4. Bernard Dwork
    Pages 14-32
  5. Bernard Dwork
    Pages 33-47
  6. Bernard Dwork
    Pages 48-72
  7. Bernard Dwork
    Pages 73-91
  8. Bernard Dwork
    Pages 92-107
  9. Bernard Dwork
    Pages 108-109
  10. Bernard Dwork
    Pages 110-112
  11. Bernard Dwork
    Pages 113-136
  12. Bernard Dwork
    Pages 159-167
  13. Bernard Dwork
    Pages 168-174
  14. Bernard Dwork
    Pages 175-177
  15. Bernard Dwork
    Pages 178-183
  16. Bernard Dwork
    Pages 184-194
  17. Bernard Dwork
    Pages 220-231
  18. Bernard Dwork
    Pages 232-241
  19. Bernard Dwork
    Pages 242-249
  20. Bernard Dwork
    Pages 250-256
  21. Bernard Dwork
    Pages 257-263
  22. Bernard Dwork
    Pages 264-271
  23. Bernard Dwork
    Pages 272-279
  24. Bernard Dwork
    Pages 280-285
  25. Back Matter
    Pages 287-312

About this book

Introduction

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 ..... .

Keywords

Equations Hypergeometrische Differentialgleichung differential equation logarithm p-adische Analysis

Authors and affiliations

  • Bernard Dwork
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4613-8193-8
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4613-8195-2
  • Online ISBN 978-1-4613-8193-8
  • Series Print ISSN 0072-7830
  • Buy this book on publisher's site
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