Bibliothèque de L'IMIST/CNRST

Includes bibliographical references (pages 423-424) and index.

1. p-adic Numbers -- 1. The Ring Z[subscript p] of p-adic Integers -- 2. The Compact Space Z[subscript p] -- 3. Topological Algebra -- 4. Projective Limits -- 5. The Field Q[subscript p] of p-adic Numbers -- 6. Hensel's Philosophy -- Appendix: The p-adic Solenoid -- 2. Finite Extensions of the Field of p-adic Numbers -- 1. Ultrametric Spaces -- 2. Absolute Values on the Field Q -- 3. Finite-Dimensional Vector Spaces -- 4. Structure of p-adic Fields -- Appendix: Classification of Locally Compact Fields -- 3. Construction of Universal p-adic Fields -- 1. The Algebraic Closure Q[subscript p][superscript a] of Q[subscript p] -- 2. Definition of a Universal p-adic Field -- 3. The Completion C[subscript p] of the Field Q[subscript p][superscript a] -- 4. Multiplicative Structure of C[subscript p] -- Appendix: Filters and Ultrafilters -- 4. Continuous Functions on Z[subscript p] -- 1. Functions of an Integer Variable -- 2. Continuous Functions on Z[subscript p] -- 3. Locally Constant Functions on Z[subscript p] -- 4. Ultrametric Banach Spaces -- 5. Umbral Calculus -- 6. Generating Functions -- 5. Differentiation -- 1. Differentiability -- 2. Restricted Formal Power Series -- 3. The Mean Value Theorem -- 4. The Exponentiel and Logarithm -- 5. The Volkenborn Integral -- 6. Analytic Functions and Elements -- 1. Power Series -- 2. Zeros of Power Series -- 3. Rational Functions -- 4. Analytic Elements -- 7. Special Functions, Congruences -- 1. The Gamma Function [Gamma][subscript p] -- 2. The Artin-Hasse Exponential -- 3. The Hazewinkel Theorem and Honda Congruences -- Basic Principles of Ultrametric Analysis.