Lectures on p-adic Differential Equations [1 ed.] 0387907149, 9780387907147

The present work treats p-adic properties of solutions of the hypergeometric differential equation d2 d ~ ( x(l - x) dx

218 114 2MB

English Pages 310 [317] Year 1982

Table of contents :
Front Matter....Pages i-viii
Introduction....Pages 1-7
The Space L (Algebraic Theory)....Pages 8-13
Dual Theory (Algebraic)....Pages 14-32
Transcendental Theory....Pages 33-47
Analytic Dual Theory....Pages 48-72
Basic Properties of ψ Operator....Pages 73-91
Calculation Modulo p of the Matrix of α f,h ....Pages 92-107
Hasse Invariants....Pages 108-109
The a → a ′ Map....Pages 110-112
Normalized Solution Matrix....Pages 113-136
Nilpotent Second-Order Linear Differential Equations with Fuchsian Singularities....Pages 137-144
Second-Order Linear Differential Equations Modulo Powers of p ....Pages 145-158
Dieudonné Theory....Pages 159-167
Canonical Liftings ( l ≥ 1)....Pages 168-174
Abelian Differentials....Pages 175-177
Canonical Lifting for l = 1....Pages 178-183
Supersingular Disks....Pages 184-194
The Function τ on Supersingular Disks ( l = 1)....Pages 195-201
The Defining Relation for the Canonical Lifting ( l = 1)....Pages 202-219
Semisimplicity....Pages 220-231
Analytic Factors of Power Series....Pages 232-241
p -adic Gamma Functions....Pages 242-249
p -adic Beta Functions....Pages 250-256
Beta Function as Residues....Pages 257-263
Singular Disks, Part I....Pages 264-271
Singular Disks, Part II. Nonlogarithmic Case....Pages 272-279
Singular Disks, Part III. Logarithmic Case....Pages 280-285
Back Matter....Pages 287-312

Lectures on p-adic Differential Equations [1 ed.]
0387907149, 9780387907147

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Bernard Dwork (auth.)

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