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Lectures on p-adic Differential Equations

Author: Bernard Dwork
Publisher: New York, NY : Springer New York, 1982.
Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 253.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Bernard Dwork
ISBN: 9781461381938 1461381932
OCLC Number: 852792709
Description: 1 online resource (310 pages).
Contents: 1. The Space L (Algebraic Theory) --
2. Dual Theory (Algebraic) --
3. Transcendental Theory --
4. Analytic Dual Theory --
5. Basic Properties of? Operator --
6. Calculation Modulo p of the Matrix of?f, h --
7. Hasse Invariants --
8. The a? a? Map --
9. Normalized Solution Matrix --
10. Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities --
11. Second-Order Linear Differential Equations Modulo Powers of p --
12. Dieudonné Theory --
13. Canonical Liftings (l? 1) --
14. Abelian Differentials --
15. Canonical Lifting for l = 1 --
16. Supersingular Disks --
17. The Function? on Supersingular Disks (l = 1) --
18. The Defining Relation for the Canonical Lifting (l = 1) --
19. Semisimplicity --
20. Analytic Factors of Power Series --
21. p-adic Gamma Functions --
22. p-adic Beta Functions --
23. Beta Functions as Residues --
24. Singular Disks, Part I --
25. Singular Disks, Part II. Nonlogarithmic Case --
26. Singular Disks, Part III. Logarithmic Case --
Index of Symbols.
Series Title: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 253.
Responsibility: by Bernard Dwork.

Abstract:

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  Read more...

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