Description
Book SynopsisThe 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. Contents 1 Introduction . . . . . . . Transcendental Theory . Hasse Invariants . The a --+ a' Map .
Table of Contents1. 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.
